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UNITED STATES OF AMERICA. 






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NORMAL 



METHODS OF TEACHING 



CONTAINING 



A BRIEF STATEMENT OF THE PRINCIPLES AND METHODS OF THE SCIENCE AND 

ART OF TEACHING, FOR THE USE OF NORMAL CLASSES AND PRIVATE 

STUDENTS PREPARING THEMSELVES FOR TEACHERS, 



EDWARD BROOKS, Ph.D., 

PRINCIPAL OF STATE NORMAL SCHOOL, MILLBRSVILLK, PENNSYLVANIA, AND AUTHOR 
OF A NORMAL SERIES OF MATHEMATICS. 



"Thai divine and beautiful thing called Teaching." 
^*The object of all education is to teach people to think for themselves." 






LANCASTER, PA.: %^0f w»'^^H\^^^ 

NOUMAL PUBLISHING COMPANY. 

1879. 



.68r 



Copyright, 1879, 
By EDWAKD BKOOKS, A. M. 



BY THE SAME AUTHOR. 

I. The Normal Series of Arithmetics. 

1. The Standard Series; a full course. 

^our books; New Primary 22; Elementary 45; New Mental 
35; New Written 80. 

2. The Union Series : a shorter course. 

Two hooks; Union Part I, 25; The Normal Union 90. 

II. Normal Elementary Algebra, §1.10 

III. Normal Geometry and Trigonometry, - 1.10 

IV. Normal Higher Arithmetic, 1.25 

. V. The Philosophy of Arithmetic. - - . - 2.25 
VI. Keys containing Methods and Models. 

SOWER, POTTS & CO., Publishers. 

530 MARKET STREET, PHILADELPHIA. 

Copies mailed on receipt of prices annexed, and introduced into 
schools for one-third less. 



INQiriREU p. t p. CO., 

8TERE0TYPEUS t PUINTER8, 

L.VJJCA8TBR. r.\. 



5" PREFACE. 
e^ —— 

■ rpE ACHING is a Science and an Art. It embraces a system of truths 
that admit of scientific statement and may be woven together with 
the tliread of philosopliic principles. As such it may be taught like 
other sciences and arts, and may thus be presented in a book to be 
studied. The present volume is the result of an earnest attempt to give 
a scientific statemejit to the subject in a form that can be used in the 
training of teachers. 

Object. — The work is designed as a Text-Book on Teaeldng. It is a 
work to be studied and mastered by those who are preparing themselves 
to teach in our public shools. Several good books on the subject have 
been written from the standpoint of the profession for professional 
readers ; this work is Avritten from the standpoint of the class-room, 
for those who are being trained for the profession. Its- design is not so 
much to adorn the literature of the profession as to aid in building up 
the profession. The aim has been to prepare a work suitable for the 
use of the classes in our Normal Schools, — a work that can be studied 
and recited like a text-book on grammar or arithmetic. 

Origin. — The work grew up in the class-room. The matter was 
originally prepared for my own "teaching classes," and has been used 
by them for many years. Primarily, it was given orally to the classes, 
the pupils being required to write down only the leading defini- 
tions and principles and an outline of the discussions. Recently 
it became necessary to divide these classes and place them in charge 
of assistant teachers. For the use of these assistants the notes were 
expanded into a little treatise which the pupils were required to copy 
and recite. So inconvenient was this, and so much valuable time was 
lost, that I resolved to comply with the request of teachers and pupils 
and put the matter in a form for publication. 

Importance.— The need of such a text-book cannot be questioned. 

Ciiij 






Copyright, 1879, 
By EDWAKD brooks, A. M. 



BY THE SAME AUTHOR. 

I. The Normal Series of Arithmetics. 

1. The Standard Series ; a full course. 

"Four books; New Primary22; Elementary 45; New Mental 
35 ; New- Written 80. 

2. The Union Series ; a shorter course. 

Two books ; Union Part I, 25 ; The Normal Union 90. 

II. Normal Elementary Algebra, $1.10 

III. Normal Geometry and Trigonometry, - 1.10 

IV. Normal Higher Arithmetic, 1.25 

, V. The Philosophy of Arithmetic. . . . . 2.25 
VI. Keys containing Methods and Models. 

SOWER, POTTS & CO., Publishers. 

530 MARKET STREET, PHILADELPHIA. 

Copies mailed on receipt of prices annexed, and introduced into 
schools for one-third less. 



INQUIRER p. 4 p. CO., 

STEUKOTYPEIIS 4 PUINTKB8, 

LANCASTER. PA. 



Z^ PREFACE. 

\r7 

' rpE ACHING is a Science and an Art. It embraces a system of truths 
that admit of scientific statement and may be woven together with 
the thread of philosophic principles. As such it may be taught like 
other sciences and arts, and may thus be presented in a book to be 
studied. The present volume is the result of an earnest attempt to give 
a scientific statemejat to the subject in a form that can be used in the 
training of teachers. 

Object. — The work is designed as a Text-Book on Teacliinq. It is a 
work to be studied and mastered by those who are preparing themselves 
to teach in our public shools. Several good books on the subject have 
been written from the standpoint of the profession for professional 
readers ; this work is written from the standpoint of the class-room, 
for those who are being trained for the profession. Its- design is not so 
much to adorn the literature of the profession as to aid in building up 
the profession. The aim has been to prepare a work suitable for the 
use of the classes in our Normal Schools, — a work that can be studied 
and recited like a text-book on grammar or arithmetic. 

Origin. — The work grew up in the class-room. The matter was 
originally prepared for my own "teaching classes," and has been used 
by them for many years. Primarilj', it was given orally to the classes, 
the pupils being required to write down only the leading defini- 
tions and principles and an outline of the discussions. Eecently 
it became necessary to divide these classes and place them in charge 
of assistant teachers. For the use of these assistants the notes were 
expanded into a little treatise which the pupils were required to copy 
and recite. So inconvenient was this, and so much valuable time was 
lost, that I resolved to comply with the request of teachers and pupils 
and put the matter in a form for publication. 

Importance.— The need of such a text-book cannot be questioned. 

(iii) 



The subject itself demands it. Teaching is a science and an art, and 
as such deserves to be stated in a scientific form. The teacirers and 
students of Teaching demand it. The time has- gone by when talks 
and lectures on the subject of Teaching will meet the wants of Normal 
instruction. The pupils need a book which they can study and recite; 
they want to see that they are making actual progress in Teaching as 
in other branches. In our Normal Schools the science of Teaching 
must be placed alongside of the other branches for exactness of state- 
ment, if it is to be respected and appreciated by students. Close study 
of mathematics and general talks on Teaching will never give pupils 
a very high appreciation of the Science of Teaching. 

We need such a work also for the teachers not attending our Normal 
Schools. County Superintendents tell young teachers to read and study 
works on Teaching ; and the question is, what shall they study? "How 
can we prepare ourselves in the science of Teaching?" is the question 
that comes up from every part of the State. There are several excel- 
lent works oil the subject ; but they do not seem to be adapted to their 
wants. Some are too profound ; and others are deficient in systematic 
thought and statement. There seems to be no elementary text-book in 
which they can find that systematic and concise statement of definitions 
and principles and detailed description of practical methods of teaching 
the branches, which they need. It is the hope of the author that the 
present work may meet this want, and supply this demand. 

Nature and Gontents.-^A. work on Teaching should be moulded by 
the wants of the student of Teaching. The student needs a systematic 
and compreliensbve view of the entire subject, lie needs carefullj' pre- 
pared definitions and statcmeids of the different divisions and topics. 
He needs a clear and definite statement of 'principles which he may fix 
in his mind, and which become as germs to his thought and practice in 
teaching, He needs to be able to give clear and logical disrussions of 
the principles, and to show their application, to the methods adopted. 
He needs to be able to state the various methods of teaching, give illus- 
trations of these methods and show their adaptation to the ditlerent 
subjects. He needs to be drilled in the literature of teaching, to 



PREFACE. V 

acquire a vocabulary of educational expressions that convey to his 
mind definite ideas like the terms and definitions of grammar and arith- 
metic. {The student-teacher should study these until they become part 
of his educational vocabulary,! as a student of law studies Blackstone 
until he becomes habituated to legal forms of thought and expression. 

The work aims to meet all these requirements. It presents, first, a 
scheme of a complete system of education, the principles on which it is 
based, and the nature and laws of its two principal divisions, Culture 
and Instruction. I It presents, second, a detailed desci'iption of the 
methods of teaching the different branches of study. In discussing 
these Methods, it gives, first, a description of the general nature of 
each branch, and second, the methods of teaching it. The former divis- 
ion embraces a statement of the philosophical character of the branch 
and its historical developments, both of which are of great value, since 
the nature of a branch determines the method of teaching it, and the 
historic order of its growth often indicates the order in which it should 
be developed in the pupil's mind. The methods of teaching each 
branch include, first, the principles, which should guide the teacher 
in his work ; second, the several methods that may be employed, indi- 
cating the correct method ; and third, descriptions and illustrations 
for actual model lessons in the branches. 

The Style. — As the work is designed for a text-book, special pains have 
been taken to employ a simple, clear, and concise style. All rhetorical 
ornament and diffuseness of description have been carefully avoided, 
and the attempt made to reduce the matter to a scientific form, and to 
state it in brief and simple sentences suitable for recitation. The author 
has endeavored to keep his classes of pupils before his mind, and aimed 
to adapt his statements to their comprehension and powers of express- 
ion. Nearly every paragraph has been written in view of the tliought,. 
How will this answer for pupils to study and recite? The object has 
been, not to talk about the subject, but to embody the subject in lan- 
guage, and thus make a text-book on Teaching. 

Correctness of Methods. — It is believed that the principles and meth- 
ods presented are not mere theories ; nearly all of them have been 



VI PREFACE. 

tested by actual experience in the class-room. There is scarcelj' a 
method suggested that I have not either tested mj-self, or had tested by 
my teachers in our Normal or Model School : and hundreds of teachers 
have introduced them into the public schools of the State and proved 
their correctness by successful teaching. Many of the methods are used 
by the leading teachers of the country, and are generally accepted as 
correct. For any methods presented which may seem novel, and in 
advance of popular practice, I ask an impartial consideration, believ- 
ing that if tried, they will also prove to be worthy of acceptance. 

Origin of Matter. — In the preparation of the work, no attempt has 
been made to be merely original. The object has been to present the 
subject as it lies in my own mind and as it is thought it should be con- 
ceived by young people preparing to teach. The subject has devel- 
oped itself in its present form through years of reading, reflection, and 
experience ; and it is impossible to separate, even if it were necessary, 
what has been acquired from that which is the product of the author's 
own thought. Whenever I am conscious of following anything peculiar 
to another author, an acknowledgment is made ; and it is possible that 
credit should have been given in some cases where it has been with- 
held. The historical facts have been taken from various sources, and, 
in some cases, the language has been partially followed. 

In closing this preface, I desire to express the hope that the book, 
though written specially for my own pupils, may be of value to many 
of the young teachers of our country ; and that it may aid in lifting up 
the practice of teaching to a higher plane, and afford means for that 
professional culture now so generally demanded. Having written the 
work in the interests of teachers, I shall find my highest reward in the 
knowledge that it has proved a benefit to teachers, and done something 
towards building up one of the best and noblest interests of society — • 
the Profession of Teaching. 

EDWARD BROOKS. 

Normal School, Millersville, Pa. 
May 10, 1879. 



TABLE OF CONTENTS. 



Pkefaoe ......... iii 

PAKT I. 
GENERAL NATURE OF EDUCATION. 

CHAPTER I. 
TuE Nature of Education ...... 13 

CHAPTER II. 
General Principles of Education . . . . .18 

CHAPTER III. 
The Science of Teaching . . . . • .26' 

CHAPTER IV. 
The Nature of the Mind . . . . , . .31 

CHAPTER V. 
The Nature of Culture . . . , , . . 37 , 

CHAPTER VI. 
Methods of Cultivating Each Faculty . . . . .42 

CHAPTER VII. 
The Nature of Knowledge ...... 48 

CHAPTER VIII. 
The Forms of Instruction . . . . . . .53 

CHAPTER IX. 
The Order of Instruction ..... 57 

CHAPTER X. 
The Principles of Instruction. 

I. Principles Derived from the Nature of tlie Mind . . .63 

II. Prineijilos Derived from the Nature of Knowledge . . 67 

III. Principles Derived from the Nature of Instruction . . 72 

(vii) 



VIH 



CONTENTS. 



PART II, 



TEACHING THE BRANCHES. 



I. OBJECT I.ESSONS. 



CHAPTER I. 

TuE Nature of Object Lessons. 
I. Value of Object Lessons 
IL Pi-cparation for Object Lessons 
in. Method of Giving Object Lessons . 
IV. Errors to be Avoided in Object LessoiiS 
V. Course of Instruction in Object Lessons 

1. Lessons on Form 

2. Lessons on Color 

•S. Objects and their Parts . 

4. Qualities of Objects . 

5. Elements of Botany 



PAG15. 


. 79 


82 


. 83 


85 


. 85 


85 


. 86 


89 


. 91 



II. liANGUAGE. 



CHAPTER I. 
The Nature of Language .... 

I Spoken Language .... 
II. Written Language .... 

III. Course in Language 

CHAPTER II. 

Teaching a Child to Read. 

I. Methods of Teaching a Child to Read . 
II. The True Method of Teachins: a Child to Read 



93 

94 

95 

105 



107 
110 



CHAPTER III. 
Teaching the Alphabet. 

I. The Nature of the Alphabet 
II. Methods of Teaching the Alphabet 

CHAPTER IV. 
Teaching Pronunciation. 

I. Nature and Importance of Pronunciation 
II. Methods of Teaching Pronunciation 
III. Teaching Correct Pronunciation 



118 
123 



127 
129 
135 



CONTENTS. IX 

CHAPTER V. 
Teaching Orthography. page. 

I. The Nature of Ortliography ..... 146 

II. Methods of Teaching Orthography .... 153 

III. The Written Method of Teaching Orthography . . . 15.5 

IV. The Oral Method of Teaching Orthography . . . 158 
V. General Suggestions in Teaching Orthography . . .-163 

CHAPTER VI. 
Teaching Reading ....... 168 

I. The Mental Element in Reading ..... 172 

II. The Vocal Element in Reading . . . .176 

III. The Physical Element hi Reading . . . . .200 

CHAPTER VII. 
Teaching Lexicology ....... 214 

CHAPTER VIII. 
Teaching English Grammar ...... 221 

I. General Nature of the Subject ..... 223 

II. Methods of Teaching Primary Grammar .... 239 

III. Methods of Teaching Advanced Grammar . . . 266 

CHAPTER IX. 
Teaching Composition ....... 286 

I. Preparation for Composition Writing .... 288 
II. Language Lessons ....... 296 

III. The Writing of a Composition ..... 304 

III. MATHEMATICS. 

CHAPTER I. 
The Nature of Mathematics ...... 819 

CHAPTER II. 

The Nature of Arithmetic ...... 334 

I. The General Nature of Arithmetic . . . . • . 325 

II. The Language of Arithmetic ..... 339 

III. The Reasoning of Arithmetic ..... 3.34 

IV. The Treatment of Arithmetic ..... 3.39 
V. The Course in Arithmetic . . . . . .343 

CHAPTER III. 

Teaching Primary Arithmetic ..... 345 

I. Teaching Arithmetical Language . . . * . 347 

II. Teaching Addition and Subtraction .... 353 



X CONTENTS. 

PAGE. 

III. Teaching Multiplication and Division .... 359 

IV. Teaching Common Fractions ..... 367 
V. Teaching Denominate Numbers ..... 374 

CHAPTER IV. 
Teaching Mental Arithmetic. 

I. Importance of Mental Arithmetic .... 378 

11. The Nature of Mental Arithmetic . . . . .382 

III. Methods of Teaching Mental Arithmetic . . . 3S6 

CHAPTER V. 
Teaching Written Arithmetic. 

I. The Nature of Written Arithmetic .... 393 

II. Methods of Teaching Written Arithmetic . . . 398 

CHAPTER VT. 
Teaching Geometry. 

I. The Nature of Geometry ...... 404 

II. Teaching the Elements of Geomctiy .... 409 

III. Teaching Geometry as a Science ..... 423 

CHAPTER VII. 
Teaching Algebra. 

I. The Nature of Algebra ...... 433 

.II, Method of Teaching Algebra . . . . .440 

IV. PHYSICAr SCIENCE. 

CHAPTER I. 
The Nature of Physical Science • . . . . 449 

CHAPTER II. 
Teaching Geography. 

I. The Nature of Geography ..... .-460 

II. Teaching Primary Geography ..... 466 

III. Teaching Advanced Geography ..... 479 

IV. Teaching Physical Geography ..... 483 

V. HISTORY. 

CHAPTER I. 
Teaching History. 

I. The Nature of History and the Course .... 485 

II. Teaching the Elements of History .... 490 

HI. Teaching Advanced History ..... 495 



PART I. 

INTRODUCTION. 



NATURE OF EDUCATION. 



I. The Nature of Education. 

II. General Principles of Education. 

III. The Science of Teaching. 

TV. The Nature of the Mind. 

V. The Nature of Culture. 

VI. The Culture of Each Faculty. 

YII. The Nature of Knowledge. 

VIII. The Forms of Instruction. 

IX. The Order of Instruction. 

X. The Principles of Instruction. 



NORMAL 
METHODS OF TEACHING. 



CHAPTER I. 

THE NATURE OF EDUCATION. 

EDUCATION treats of the development of the powers of 
man and the furnishing of his mind with knowledge. 
The term education is derived from educare, to teach, which 
is from educere, to lead out, which is from e, out, and diccOj 
I lead. 

The primary idea of education, as shown by the origin of 
the term, seems to be the developing or drawing out of the 
powers of the mind ; and it has been supposed that this was 
its earliest use. It is said to be doubtful, however, whether 
the Romans ever used the word in this sense, though most 
modern writers have so understood it. The term has, at the 
present day, so broadened its meaning as to embrace both the 
. development of man's powers and the furnishing of his mind 
with knowledge. 

Problem of Education.— The problem of education em- 
braces several distinct elements, as will appear from the 
following analysis. First, there must be a being to be edu- 
cated ; this being is 3Ian. Second, there must be something 
with which to educate man, some material to be used in the 
educational process; this material, consisting of ideas, facts, 
truths, and sentiments, maybe called the ifa^ter of education. 

(13) 



14 METHODS OF TEACHING. 

Third, there must be some way in which these two elements 
are united in the educational process ; this way (inethodos, a 
way) gives rise to the Methods of Education. 

The problem of education is thus seen to embrace thi-ee 
elements — Man^ Matter^ and Method. Man is the subjective 
element; Matter is the objective element; and Method is the 
process by which these two are linked together in the attain- 
ment of educational results. The old problem of common 
school education has been facetiously called the problem of 
"the three E^s — readin', 'ritin', and 'rithmetic;" the real 
problem of education may be seriously called the problem of 
the three M^s — Man, Matter, Method. 

Branches of Education. — This analysis of the problem 
of education enables us to determine the fundamental branches 
of the science of education. Considering Man, the first ele- 
rnent of the problem, we see that he has susceptibilities and 
powers which may be trained and developed. The process of 
bringing forth these powers in activity, strength, and har- 
mony, we call Culture. This culture is not a thing of 
chance; there is a proper way in which it is to be given. 
The consideration of the manner in which this culture is to 
be imparted, gives rise to the first branch of the science 
called Methods of Culture, 

Considering the 3Iatter, the second element of the problem, 
we perceive that knowledge, which is a product of the mind, 
may be used in giving culture to the mind. That which 
came forth from one mind may be put into other minds, to 
call into activity the faculties by which it was originally pro- 
duced. This process of putting knowledge into the mind is 
called Instruction. The consideration of the manner in 
which instruction may be imparted gives rise to a second 
branch of the science called Methods of Instruction. 
, These two divisions. Culture and Instruction, are logically \ 
distinguished. The one seeks to draw out the powers of the , 
mind ; the other seeks to put knowledge into the mind. The 



THE NATURE OF EDUCATION. 15 

former is subjective, working from within outward ; the latter 
is objective, working from without inward. Culture aims to 
bring out power ; instruction aims to put in knowledge. 
Each, of course, implies the other. To give culture, we make 
use of knowledge : in impai'ting instruction there must be 
some growth of the mental powers. The two processes, how- 
ever, are not identical ; and the laws and methods of each are 
different. They are in fact the complements of each other ; 
the two hemispheres of the science, which, united, give it 
symmetry and completeness. 

At first thought, since culture and instruction are seen to 
embrace all possible educational processes, it would seem that 
these two branches constitute the 'entire science of education. 
A little further analysis, however, gives rise to another 
branch closely connected with these two primary branches, 
and possibly contained in them, but so important as to be 
regarded by some as coordinate with these two, and requiring 
a distinct treatment. Thus, since culture and instruction are 
to be given to a number of pupils together, called a school, 
and this school is to be organized, governed, etc., there arise 
other subjects not immediately embraced in, or at least not 
conveniently treated under, the two primary branches of the 
science. On account of the intimate relation of these several 
subjects, educators have treated them under one head, and 
regarded it as a distinct branch of the science, which has been 
appropriately named by Dr. Wickersham, School Economy. 

The science of education is thus seen to embrace three 
branches — Methods of Culture, 3Iethods of Instruction, and 
School Economy. This three-fold division- of the science is 
not new, although it is recent. It is not so much of a dis- 
coveiy as a growth. It seems to have been gradually de- 
veloping in the minds of educators for many years, and is 
now largely accepted by the profession as a logical and com- 
plete classification. 

Nature of Teaching. — The act of afibrding this culture 



If) MIO'l'IIODS OK 'I'i;AC1I1N(J. 

!iii(l iin|t;ut,iiijL;- Uiirt kii<)wl(!<l<^(; in culled Tcachimj ; mikI tlu; 
]H!rH()ii who does iluH work is cilled a Teacher. The term 
Teiiehing is also used as the name of the science and art 
of givinj? culture and instruction. Thus we speak of the 
S(Men(U! of Teaehiii}^ and tlu! Art of T(!achin<^. 

Th(! tci-iu Tciu-ldiKj, it is thus He(!ii, is a little more compre- 
hensive IIi:mi the word I iistruetioii. An Instructor, Strictly 
s|)(':\,Uiii,<f, is one who imparts kiiowledii;(! to the mind; a 
Te.'ieluM- is oru^ who imports kuowhulj^c' :uid, at the same time, 
aims l.o f;ive mental cultun;. 

Other TerniH. — The term Educator is popularly delincid as 
one who ediu-atcs or gives instru(!tion. It is more ai)propri- 
ately used, howev(!r, to denote one wlio is versed in, or. who 
advocates and promotes, education. 'IMie term J'JducaliqnisI, 
is nlso employed in this latter sense, and by msiiiy is pre- 
ferred to tlu! term Educator. 

'IMk! term I'edagoyica, or Pedaf/rxji/ (pais^ paidos, a boy, 
!uid (Kjof/os, leading or guidiui;), is used ])y (piite a large 
numlx'r of writers as tlu; name of the science and art of in- 
struction. Tlu! term is popular in Oermany, and efforts have 
been made to introduce it into this country and England; 
but so far with but little success. Jt is somewhat awkward 
and unmusical, besides which, the term pedagogue is, in both 
of these cotnitries, used as a term of reproacli. 

The term Didactics, from dida^tko^I teacli, is often used as 
the name of the science and art of teaching. 'IMie sul)je<'t has 
l)een divided into two parts : General Didactics, which 
presents the principles of teaching; iind^Hpecial Didactics, or 
Methodics, which iippiies these principles to the several 
branches of instrucitlon. 'fhe term is api)ropriate and may 
in time be adopted, but the term Teaching seenis at jiresent 
to be generally prcfi'rred. 

Kinds of liffnration. — Kdueaticni is generally divided into 
Physicid Education, Intellectual Education, and Moral and 
Iveligious Edu<'Ml ion. IMiysical Kdncntion is tlnit which jier- 



THE NATURE OK EDUCATION. 17 

tains to the body. Its object is to train eA'ery power of tlie 
body for tiie attainment of the ends of health, strength, skill, 
and beauty. 

Intellectual Education is that which pertains to the intellect. 
Its object is to develop all the mental faculties into their 
highest activity, and to furnish the mind with valuable and 
interesting knowledge. Moral Education is that which per- 
tains to the moral nature of man. Its olyect is the develop- 
ment of conscience and the subordination of the will to the 
idea of duty. Religious Education has reference to the de- 
velopment of the higher spiritual instincts and sentiments 
forming the religious nature. It is especially distinguished 
from moral education in that the former finds its motive in 
human relations and the latter in the existence of a Supreme 
Being. 

Besides these there are also several subordinate or collateral 
divisions ; as ^Esthetic Education, which refers to the culture 
of the imagination and taste ; Domestic Education, which 
refers to the education of children in the household; Common 
School Education, which refers to the education obtained in a 
common school ; Popular Education, which refers to the edu- 
cation of the people; and National Education, which refers to 
a system of education provided by the state. 



CHAPTER II. 

GENERAL PEINCIPLES OF EDUCATION. 

EDUCATION is not a matter of chance or haphazard pro- 
cedure. All development must proceed in accordance 
with some regular plan or order. There can be no organic 
growth without the control of principles determining and 
shaping the development. The plant grows in obedience to 
the laws of vegetable life ; and the development of mind, 
which is the object of education, must be controlled by the 
laws of its own being. 

A system of education must therefore be based upon 
certain broad and fundamental principles which express the 
laws of human life and development. These principles are 
not only the foundation upon which the system rests, but 
they give shape and character to the entire superstructure. 
All the great writers on education have conceived some lead- 
ing ideas and endeavored to unfold a scheme of instruction 
growing out of these fundamental conceptions. 

From a very careful surve}^ of these different schemes and 
a thoroug'h examination of the problem of education itself, 
the following principles have been reached which seem to 
contain a complete system of education. These principles, it 
is thought, embrace all the fundamental ideas of education 
from Aristotle to Pestalozzi and Froebel. The design is to 
enumerate only the general laws of education ; the particular 
laws of culture and instruction will be presented in another 
place. These principles are presented in ten propositions, 
which we may call our educational decalogue. 

1. The primary object of education is the perfection of 
the individual. The educator should understand the object 

(18) 



GENERAL PRIXCIPLES OF EDUCATION. 19 

for which he labors; for the object to a large extent de- 
termines the means and methods employed in the "work. A 
correct end in view will lead to correct methods; a false object 
will vitiate both the means and the methods of using them. 
In education, especially, the end aimed at crowns the work 
with excellence. 

The true object of education has not been generally under- 
stood by educators and parents. The ancient Greeks made a 
fundamental mistake when they based their system upon the 
pei'fection of the state rather than the individual. Parents 
to-day send their children to school to fit them for business 
or a profession, to enable them to make a good living in the 
world, or to occupy an honorable position in society. Teachers 
often seem to think more about the amount of knowledge they 
are imparting to the child than of the training of its mind 
and the development of a manly and virtuous character. All 
of these objects fall below the high ideal we should set before 
us, and degrade and injure the work of education. 

We should, therefore, remember that the true object of edu- 
cation is the perfection of the individual. We should aim for 
the perfecting of man in his entire nature, — physically, men- 
tally, and morally. The teacher should never forget that the 
highest object of his work is the fullest and most complete 
development of the immortal beings committed to his care ; 
and that his work is not only for time but for eternity. In 
other words, it shovdd be remembered that the highest object 
of education is human perfection. 

2. The perfection of the individual is attained by a har- 
monious development of all his powers. Man possesses a 
multiplicity of .capacities and powers, all of which contribute 
to his well-being and his dignity. A perfectly developed man- 
hood or womanhood implies the complete development of 
ever}- capacity and gift. These powers are so related that 
they may be unfolded in very nearly equal proportions, and 
harmoniouslv blend in the final result. For the attainment 



20 ■METHODS OF TEACHING. 

of our ideal such a development is required. The educational 
work should reach every power, and aim at a full and har- 
monious development of them all. 

This principle is limited by the existence of special talents 
and the demand for special duties. While a general scheme 
of education should seek to give culture to all the powers, we 
should not be neglectful of special and unusual gifts. Genius 
should be recognized, and our general system be so far modi- 
fied as to give opportunity for its highest development and 
achievements. An unusual gift for poetry, music, painting, 
mechanics, mathematics, etc., should be recognized, and oppor- 
tunity^ offered for its fullest development. 

We must remember also that duties are diverse as well as 
talents, and that special training is needed for the preparation 
of mankind to discharge these special duties. There must 
be farmers, and artisans, and physicians, etc., and they need 
special preparation for their work ; and educational systems 
must recognize this fact and provide for it. 

The principle of harmonious development has reference to 
that general educational prepai*ation which all persons need 
for their own personal excellence, and as a preparation for a 
special course of instruction to prepare them for specific 
duties and occupations. The general scheme of education 
should therefore aim at a full and harmonious development of 
all of man's powers. 

3. These powers develop naturally in a certain order ^ which 
should be followed in education. . Intellectual life seems to 
begin in the senses ; the child awakens into knowledge through 
sensation and perception. Then follows the action of the 
memory as a retaining and a recalling power, accompanied 
by imagination as the power of representation. After this 
come judgment and reasoning and the power of abstraction, 
generalization, and classification. Still later we become con- 
scious of the intuitive ideas and truths, and learn to work 
them up into new truths by the power of deductive thought. 



GENERAL PRINCIPLES OF EDUCATION. 21 

Last of all, the mind awakens to the consciousness of man as 
a moral and religious being, bearing relations to his fellow 
man and to God. 

Finding in man such a relation of faculties and powers, we 
should learn the order of their development and follow that 
order in our work. We should first afford food for the growth 
of the mind through the senses. We should call the memory 
into activity, and afford means for the culture of the imagina- 
tion. We should lead the mind gradually from things to 
thoughts, and give activity to judgment and reasoning, and 
also to the powers of abstraction and generalization. Desires 
should be awakened and dii-ected. the affections unfolded, and 
the will be subordinated to the ideas of truth and duty 

Though these powers develop in a certain order, it is not 
to be thought that the activity of one waits upon the full 
development of another. To a certain extent they are all 
active at the same time ; but they are active in different de- 
grees. The order given represents the relative activity, and 
thus indicates the relative attention required to be given them 
in the work of education. Such a relation should be clearly 
understood by the educator, and should guide him in his work. 

4. The basis of this development is the self-activity of the 
child. Education is a spiritual growth, and not an accre- 
tion. It is a development from within, and not an aggrega- 
tion from without. For this growth there must be forces 
working within the child. This force is the self-activity of 
the soul, going out towards an object as well as receiving 
impressions, from it ; gaining power in the effort, and work- 
ing up into organic products the knowledge thus acquired. 

The object of education is to stimulate and direct this 
natural activity. The teacher, therefore, should never do for 
the child what it can do for itself. It is the child's own 
activity that will give strength to its powers and increase the 
capacity of the mind. The teacher must avoid telling too 
much, or aiding the child too frequently. A mere libit or 



22 METHODS OF TEACII1^■G. 

suggestive question to lead tlie mind in the proper direction 
is worth much more than direct assistance, for it not only 
gives activity and consequently mental development, but it 
cultivates the power of original investigation. 

We should aim to cultivate a taste and desire for knowledge 
on the part of the child, so that this activity may be natural 
and healthful. To force the mind to the reception of knowl- 
edge is not education, it is cramming ; and the object of educa- 
tion is not cram but culture. For the attainment of the high 
end of education, therefore, we must depend on the self- 
activit}' of the child ; and it is the teacher's office to excite 
and direct this activit3\ 

5. This self-activity has two distinct j^hases; from without 
inward^ — receptive and acquisitive; and from within out- 
ward, — loroductive and expressive. First, the mind is re- 
ceptiA'e of knowledge. Objects of the materialworld make 
their impressions \ipon the senses, and ideas and thoughts 
spring up in the mind. Knowledge thus comes into the mind 
from without through the senses. The contents of books also 
flow into the mind through written language, and are treas- 
ured in the memor\-. In all this the mind is receptive, the 
process is from without inward, and the result is acquisition, 
learning. 

The mind is also active in creating as well as in receiving. 
It has the power to reproduce as well as to receive. In its 
self-activit}' it can take the material thus acquired, and work 
it up into new products. It can also send it forth on the 
stream of clear and definite expres'^n in audible or visible 
speech. It thus works from witbiij outward, creating, and 
evolving what it creates. 

The mind in its receptive phase is said to be intuitive ; 
that is, the knowledge comes directly into the mind. The 
mind in the second phase is called elaborative, because it 
works up the material into new products. This distinction 
has also an educational significance. 



GENERAL PRINCIPLES OF EDUCATIOX. 23 

6. These two phases, the receptive and productive, should 
go hand in hand in the ivork of education. This is evident 
from their natural correlation. The activity of the mind in 
receiving naturally creates the correlative activity of produc- 
ing. The knowledge coming into the mind through the re- 
ceptive capacity excites the mind to a productive activity. 
It acts like food in the stomach, which excites the powers of 
digestion and assimilation. Besides, the knowledge gained 
by the receptive powers becomes the material for the produc- 
tion of the creative powers. This material is operated upon 
and worked up into new products. 

These two operations are not to be separated in education. 
Each gives life and vigor to the other. The receptive powers 
are stimulated by the activity of the productive powers, and 
the productive powers are set into immediate activity by the 
presence of receptive knowledge. They thus play into each 
other's hands, act as a mutual stimulus to each other, and 
should go hand in hand in the work of education. 

1. There must he objective realities to supply the conditicn 
for the self-activity of the mind. The mind cannot act upon 
itself alone ; there must be food for the mental appetite. There 
must be an external world of knowledge to meet the wants of 
the internal knowing subject. 

Such an external world is supplied. There is a world of 
knowledge suited to and correlating with-the wants of the soul. 
The objective world of nature is found to be an embodiment 
of thought, and this thought developed into science meets the 
wants of the active spirit. There is also the great world of 
space and number, Wi^. .s ideas and truths ; and also the 
loftier abstractions of the True, the Beautiful, and the Good. 

This world of knowledge is adapted to every power and 
capacity of the mind. This is evident, since knowledge is the 
product of the mind operating upon external realities. Knowl- 
edge as the product of one mind must be suited to the differ- 
ent capacities of all other minds. It is thus seen that there 



24 ^lETliODS OF TEACIIIXG. 

is abundant provision for the activity and growth of all of 
the powers of the mind. 

8. Education is not creative ; it only assists in developing 
existing possibilities into realities. The mind possesses in- 
nate powers. These may be awakened into a natural activit}'. 
The design of education is to aid nature in unfolding the 
powers she has given. No new power can be created by edu- 
cation; the object is to arouse those which exist to a health- 
ful activity, and to guide them in their unfolding. In other 
words, the object of education is to aid nature in unfolding 
the possibilities of the child into the highest possible realities. 

9. Education should be modified by the different tastes and 
talents of the pupil. All minds possess the same general 
capacities or powers. These powers are, however, possessed 
in different degrees. An vinusual gift of any one or more 
powers constitutes genius. Tastes or dispositions for par- 
ticular branches of science or art also differ. 

Such differences should not be overlooked in a scheme of 
education. While all should receive a course of general cul- 
ture, opportunity should be given for the development of 
special tastes and gifts. It is these which enrich science and 
art, and add to the sum of human knowledge ; and the pro- 
gress of science and art- demands that genius shall have the 
most abundant opportunities for its fullest and highest devel- 
opment. 

10.. A scheme of education should aim to attain the triune 
results — development, learning, and efficiency. Development 
relates to the culture and growth of the powers of the child. 
This is the fundamental idea of education, and is of primary 
importance. Education has reference also to the acquisition 
of knowledge. It aims to enrich the mind with the truths of 
science, to make a man learned, to produce scholars. 

A third object is the acquisition of skill in the use of culture 
and knowledge. It is not enough that the mind has well-devel- 
oped powers and is richly furnished with knowledge. There 



GENERAL PRINCIPLES OF EDUCATION. 25 

should be the power to make use of this culture and knowl- 
edge. The educated man should be able to do as well as to 
think and knoio. This third design'of the educator, the attain- 
ment of skill, should not therefore be overlooked. The true 
aim of education is thus seen to be the attainment of the three 
ends — culture, knowledge, and efficiency. 
2 



CHAPTER III. 



THE SCIENCE OF TEACHING. 



TEACHING, as a science, treats of the Laws and Methods 
of human Cultui-e and Instruction. The term is derived 
from the Saxon word tcecayi, which meant to show, to teach, 
and is allied to the Greek deikniinai^ to show, and the Latin 
docere, to teach. 

Primarily, the word appears to have meant very nearly the 
same as the word instruction ; though even in its primary sense 
of directing or showing, it is suggestive of the act of develop- 
ing the mind as well as instructing it. At the present day. 
Teaching embraces both Culture and Instruction, — the bring- 
ing out and training of the powers, as well as the furnishing 
of the mind with knowledge. A true teacher seeks to culti- 
vate the minds of his pupils as well as to instruct them. 

Laws and 3lefhods. — The definition of Teaching embraces 
four distinct and prominent ideas, — Laivs, Methods, Culture, 
and Instruction. By Laws we mean the principles that guide 
us in an operation. Thus, in grammar, the principle that the 
verb agrees with its subject in niimber and person, will guide 
us in speaking and writing correctly. So the principles of 
numbers enable us to operate with them correctly' in applj'ing 
them to the business transactions of life. 

By Methods we mean the manner of performing an opera- 
tion. Thus, in arithmetic we have the methods of subtracting, 
of finding the greatest common divisor, etc. The rules of 
arithmetic are statemelits of methods of operation. So also 
in education, there are methods of doing things or of obtaining 
certain results. There are methods of giving culture to the 
different faculties, and also of teaching the diff'oront branches. 

(26) 



THE SCIENCE OF TEACHIXQ. 27 

The relation of Laws and Methods should be clearly under- 
stood. Principles are self-existent, or belong to the very na- 
ture of the subjects ; Methods are derived from principles ; 
they are the outgrowth of laws or principles. Principles are 
of more value than methods ; if you know the principle, you 
can derive the method, though you may know the method 
without understanding the principle. One who is familiar 
with principles is thus much more independent than one who 
knows only methods. These relations of principles and 
methods may be illustrated in arithmetic and grammar, and 
in other school studies. 

Culture and Instruction. — Culture is the developing of 
the powers of man. The tei^m is derived from colo^ I culti- 
vate, and derives its educational meaning from the act of tilling 
and enriching the soil. It has reference to the development 
and improvement of any of man's faculties or powers. To 
awaken the mind into activity, to call out and mould its vari- 
ous faculties, to train the eye to see, the memory to retain 
and recall, the understanding to think and reason, etc., — this 
is to cultivate the mind. 

Instruction is the imparting of knowledge to the mind. It 
is the process of transferring knowledge from one mind to 
another. The term is derived from in, into, and struo, I 
build, meaning, I build into. To instruct the mind is thus to 
put knowledge into it, to build up knowledge in the mind. 
The instructor takes the knowledge that is in his own mind, 
and, without losing it himself, puts it into the mind of his 
pupils, and builds it up there, as an architect erects a temple, 
in symmetry and proportion. 

The relation of Culture and Instruction should be clearly 
understood. The object of Culture is to strengthen and de- 
velop the mind ; the object of Instruction is to put knowledge 
into the mind. Culture gives a person mental power ; Instruc- 
tion gives him information or learning. They are both impor- 
tant ; but Culture is more important than mere Instruction. 



28 



METHODS OF TEACHING. 



To be able to acquire knowledge is worth uiH-e than the knowl- 
edge we have acquired. The ability to originate knowledge is 
even more important. A person should know more than he 
ever learned ; and this is possible when his powers have been 
cultivated. The object of the teacher, therefore, should be not 
merely to impart knowledge, but to cultivate mental power. 

Teafhing a Science. — Teaching is both a science and an 
art. That it is a science, which has boon questioned, will 
appear from the following considerations: To constitute a sci- 
ence we must have three things: 1. Knowledge; 2. Knowl- 
edge systematized ; 3. Principles showing the relations of this 
knowledge, and binding it together into an organic unity. 
There is a knowledge of teaching, as is attested by the many 
works and articles written upon the subject. This knowledge 
can be s}' stematized as logically as the knowledge of grammar 
or arithmetic. There are also fundamental principles of teach- 
ing, which exjDress the laws of culture and instruction. Hence, 
from the definition of a science, we can claim that there is a 
science of teaching. 

Branches of Teaching. — The Science of Teaching is 
divided into three branches ; Methods of Culture^ Methods of 
Instruction, and School Economy. This three-fold division 
embraces everything that pertains to teaching, and is therefore 
regarded as exhaustive. Indeed, as previously stated, since 
man can only be cultured and instructed, it would seem that 
there could be only two distinct branches, Methods of Cul- 
ture and Methods of Instruction ; but since this work is to be 
done Avith the pupils organized into a school, and since such 
an organization gives rise to special regulations and provis- 
ions, there incidentally arises a third division, called School 
Economy. 

Methods of Culture treats of the nature of the powers of 
man, and how to develop them. It embraces three general 
divisions: 1. The Nature of Man ; 2. The Nature of Culture; 
3. The Methods of Cultivating each Faculty. In a full treat- 



THE SCIENCE OF TEACHING. 29 

ise upon this subject, each one of these topics should be dis- 
cussed in detail. 

Methods of Instruction treats of the different branches of 
knowledge and how to teach them. It embraces three general 
divisions: 1. The Nature of Knowledge; 2. The Nature of 
Instruction ; 3. The Methods of Teaching each Branch. In a 
full treatise upon the subject, each one of these topics should 
be discussed in detail. 

The three divisions of these two branches of Teaching, are 
seen to correlate. Thus the Nature of Man in the first branch 
correlates with the Nature of Knowledge in the second ; the 
Nature of Culture in the former corresponds to the Nature of 
Instruction in the latter; and the Method of Cultivating each 
Power is correlative with the Method of Teaching each 
Branch. As the two branches stand in the relation of the 
subjective and the objective, so do the corresponding divi- 
sions of the two branches. 

School Economy treats of the methods of organizing and 
managing a school. It embraces five things: 1. School Pre- 
paration; 2. School Organization; 3. School Employments ; 
4. School Government ; 5. School Authorities. This classifi- 
cation is that presented by Dr. Wickersham, and is regarded 
as logical and complete. 

The relation of the several branches of the Science of 
Teaching, together with a few of their practical divisions, are 
expressed in the following outline : 

r Nature of Man. 
1. Methods of Culture. - Nature of Culture. 

L Method of Cultivating each Faculty. 

{Nature of Knowledge. 
Nature of Instruction. 
Method of Teaching each Branch. 

r Scliool Preparation. 
I School Organization. 
3. School EcoJiOMY. \ School Emidoyments. 

I School Government. 
[ School AutJiorities. 



u ^ W 



H 



H 



30 METHODS OF TEACHING. 

In this work we design to speak mainly of Methods of 
Instruction, but so necessary is a knowledge of the mind and 
the methods of training it that we shall give a single chapter 
to each of the three divisions of Methods of Culture; namely, 
The Nature of Mind, the Nature of Culture, and the Methods 
of Cultivating each Faculty. We shall then speak of the 
Nature of Knowledge and the Nature of Instruction, embrac- 
ing under the latter head. Forms of Instruction, Order of 
Instruction, and Principles of Instruction. Having laid this 
foundation, we shall proceed to the consideration of the 
Methods of Teaching each Branch of Knowledge. 



CHAPTER IV. 

THE NATURE OF THE MIND. 

rpHE Mind is that which thinks, feels, and wills. It is that 
-L immaterial principle which we call the soul, the spirit, 
or the intelligence. Of its essence or substance, nothing is 
known ; we know it only by its activities and its operations. 
The different forms of activity which it presents, indicate 
diiferent mental powers, which are called Faculties of the 
mind. 

A Mental Faculty is a capacity for a distinct form of 
mental activity. It is the mind's power of doing something, 
of putting forth some energy, of manifesting itself in some 
particular manner. The mind possesses as many faculties as 
there are distinct forms of mental activity. In order, there- 
fore, to ascertain the different faculties of the mind, we must 
notice carefully the various waj'S in which the mind acts. 

General Classification. — The mind embraces three general 
classes of faculties; the Intellect^ the Sensibilities^ and the 
Will. Every capacity or power which the mind possesses falls 
under one of these three heads. Every mental act is an act of 
the Intellect, the Sensibilities, or the Will. 

The mind is thus a tri-unity, — one substance with a trinity 
of powers. The doctrine of the Trinity is as evident in the 
creature as in the Creator. Made in the image of God, the 
mind reflects the nature of the divine pattern after which it 
was fashioned. As in God we have the Father, the Son, and 
the Holy Spirit ; so in man we have the Intellect, the Sensi- 
bilities, and the Will. / 

The Intellect is the power by which we think and Icnow. 
Its products are ideas and thoughts. An Idea is a single 

(31) 



32 METHODS OF TEACHING. 

notion, which may be expressed in one or more words, not 
forming a proposition ; as, a man, an animal, etc. A Thought 
is the combination of two or more ideas, which when ex- 
pressed in words, gives us a proposition; as, a man in an 
animal. 

The Sensibilities are the powers by which we feel. Their 
products are emotions, affections, and desires. An emotion is 
a simple feeling, as the emotion of joy, sorrow, etc. An affec- 
tion is an emotion that goes out towards an object ; as love, 
hate, envy, etc. A desire, is an emotion that goes out to an 
object with the wish of possession ; as the desire of icealth, 
fame, etc. 

The Will is the power by which we resolve to do. It is 
the executive power of the mind, the power by which man 
becomes the conscious author of an intentional act. The 
products of the Will are volitions and voluntary actions. It is 
in the domain of the Will that man becomes a moral and 
responsible being. 

The relation of these three spheres of activity may be illus- 
trated in a variety of ways. I read of the destitution and 
suffering in a great city and understand the means taken for 
their relief; this is an act of the intellect. I feel a deep sym- 
pathy with this suffering ; my heart is touched with pity, and 
I experience a strong desii'e to aid in relieving their distress,; 
this is an act of the sensibilities. I desire to express my 
feelings of pity and follow my sense of duty, and resolve to 
aid them by sending a contribution or going personally to 
their relief; this is an act of the will. 

TJie Intellect. — The Intellect embraces several distinct 
faculties; Perce/ption, Memory, Imagination, Understanding, 
and Intuition, or the Reason. This classification of the Intel- 
lect is now almost universally accepted, though writers occa- 
sionally differ in tlie terms they use to name the different 
powers. 

Perception is the power by which we gain a knowledge of 



I 



NATURE OF THE MIND. 33 

external objects through the senses. It is the faculty by which 
we gain a knowledge of objects and their qualities. Its pro- 
ducts are ideas of external objects and of the qualities of ob- 
jects. The ideas which we possess of persons, places, things, 
etc., are mainly given by perception. 

Memory is the p<jwer by which we^ retain and recall knowl- 
edge. It enables us to hold fast to the knowledge we have 
acquired, and also ) recall it when we wish to use it. These 
two offices of the .\I mory are distinguished as [Retention and 
Recollection.) By some writers these are regarded as separate 
faculties; and othtis again discard the element of retention. 
Besides these, the memory also gives us a repreaentatioyi of 
that which it recalls, and recognizes it as something of our 
past experience. 

Imagination is the power by which we form ideal concep- 
tions. It is the power of forming mental images by uniting 
different parts of objects given by perception, and also of 
creating ideals of objects different from anything we have per- 
ceived. Thus, I can conceive of & /lying horse by uniting my 
ideas of wings and a horse ; or I can imagine a landscape or 
a sti-ain of music different from anything I have ever seen or 
heard. Imagination is thus the power of ideal creation. 

Tlie Unukestandino is the power by which we compare ob- 
jects of thought and derive abstract and general ideas and 
truths. It is the olaborative power of the mind; it takes 
the materials furnished by the other faculties and works them 
up into new products. Its products are abstract and general 
ideas, truths, laws, causes, etc. 

Intuition, or the Reason, is the power which gives us ideas 
and thoughts not furnished by the senses nor elaborated by 
the Understanding. Its products are called primary ideas 
and primary truths. The Primary Ideas are such as Space, 
Time, Cause, Identity, the True, the Beautiful, and the Good. 
The Primary Truths are all self-evident truths, as the axioms 
of mathematics and logic. 
2* 



34 METHODS OF TEACHINQ. 

The Understanding. — The Understanding embraces sev- 
eral distinct faculties or forms of mental activity. These are 
Abstraction, Conception, Judgment, and Reasoning. This 
division is now almost universally adopted, and the same 
terms are employed by nearly all modern writers. 

Absteaction is the power of forming abstract ideas. It is 
the power by which the mind draws a quality away from its 
object, and makes of it a distinct object of thought. Its pro- 
ducts are abstract ideas, such as hardness, softness, color, etc. 
The naming of abstract ideas gives us abstract terms. The 
term Abstraction is derived from ab, from, and traho, I draw, 
and signifies a drawing from. 

Conception is the power of forming general ideas. By it 
we take several particular ideas, and unite their common prop- 
erties, and thus form a general idea which embraces them all. 
The products of Conception are general ideas, or ideas of 
classes ; as horse, bird, man, etc. The naming of general 
ideas gives us common terms. This faculty is often called 
generalization ; but the term Conception is more appropriate, 
and is the one generally adopted by logicians. The term 
Conception is derived from con, together, and capio, I take ; 
and signifies a taking together. 

Judgment is the power of perceiving the agreement or disa- 
greement of two objects of thought. It is the power of com- 
parison. It compares one object directly with another, and 
gives us a proposition. A proposition is a judgment ex- 
pressed in words. Thus, a bird is an animal, is a judgment 
expressed. The term Judgment is applied to both the mental 
faculty and its product. 

Reasoning is the power of comparing two ideas through 
their relation to a third. It is a process of indirect or medi- 
ate comparison. It deals with three objects of thought and 
requires three propositions. Thus, suppose I wish to com- 
pare A and B, and perceiving no relation between them, see 
that A equals C, and B equals C, and thus infer that A equals 
B ; such an inference is an act of reason injr. 



NATURE OF THE MIND. 35 

The form in which reasoning is expressed is called a Syllo- 
gism. A Syllogism consists of three propositions so related 
that one of them is an inference from the other two. Two of 
these propositions are called the premises and the third the 
conclusion. Thus, in the above example the two propositions, 
"A equals C" and "B equals C," are the premises; and "A 
equals B" is the conclusion. 

Reasoning is of two kinds; Inductive Reasoning and Z)e- 
ductive Reasoning. Inductive Reasoning is the process of 
deriving a general truth from particular truths. Thus, if I 
find that heat expands several metals, as zinc, iron, copper, 
etc., I may infer that heat will expand all Tnetals. Such an 
inference of a general truth from the particular facts is called 
Induction. Inductive Reasoning proceeds upon the principle 
that what is true of the many is true of the whole. 

Deductive Reasoning is the process of deriving a particu- 
lar truth from a general truth. Thus, from the general propo- 
sition that heat expands all metals, I may infer by Deduction 
that heat will expand any particular metal, as silver. Deduc- 
tion proceeds upon the principle that what is true of the whole 
is true of the parts. 

Other Forms of Mental Activity. — Besides the faculties 
now named, there are two other forms of mental activity, or 
mental states, called Consciousness and Attention. These ai-e 
not regarded as specific faculties of the. mind, but as condi- 
tions or accompaniments of these faculties. 

Consciousness. — Consciousness is the power or attribute of 
the mind by which it knows its own states or actions. The 
term is derived from con, with, and scio, I know, and means a 
knowing with the mental acts or states. It is regarded as an 
attribute of the mind, involved in the very idea of mind, and 
not as a mental faculty. Thus, to kiiow is to know we know, 
to feel is to know we feel, to will is to know we will. The 
expressions, " I know that I know," " I know that I feel," 
etc., are equivalent to I am conscious that 1 know, I am con- 



36 METHODS OF TEACHING. 

scious that I feel, etc. Consciousness is a kind of inner light 
by which one knows what is going on within his mind ; it is a 
revealer of the internal phenomena of thought, feeling, and 
will. 

Attention. — Attention is the power of directing the mind 
voluntarily to any object of thought to the exclusion of 
others. It is the power of selecting one of several objects, 
and concentrating the mental energies upon it. The term is 
derived from ad, to, and tendo, I bend, which was probably 
suggested by the attitude of the body in listening attentively 
to a sound. 

Attention is not a distinct form of mental activity, but is 
involved in and underlies the activity of all the faculties. 
The voluntary operation of any of the mental powers, as Per- 
ception, Memory, etc., carries with it an act of attention. It 
is not the power of knowing, but of directing that which may 
know. It has no distinct field or province of its own, yet 
without it the faculties would be of little use to us. It works 
with them and through them, increasing their efflcienc}?^, and 
giving them a power they would not otherwise possess. 

Conception. — The term Conception is often used in a gen- 
eral and popular sense, meaning that power which the mind 
has of making anything a distinct object of thought. In this 
sense it is intimately related to all the mental faculties. Thus 
I can conceive of a tre» or a horse which I have seen, a land- 
scape which I may not have seen, a proposition in geometry, 
a truth in natural philosophy'', etc. Some writers have used 
the term in a more specific sense, as the power of forming an 
exact transcript of a past perception. In Logic the term is 
restricted to the power of forming general ideas, as we have 
previously defined it. 



CHAPTER V. 

THE NATURE OF CULTURE. 

CULTURE, as alreadj^ defined, is the developing of the 
powers of man. It aims at the unfolding and growth of 
all the powers, and the training of them so as to attain their 
highest activity and fullest development. As in the culture 
of land we aim to improve the soil, so in human culture we 
aim to enrich the soil of the mind and cause it to bud and 
blossom and bring forth its richest harvests of thought and 
sentiment, of science, art, and character. 

Culture is usually divided into three distinct branches; 
Physical Culture, Intellectual Culture, and Moral and Relig- 
ious Culture. Besides these there are also Social Culture, 
Jj^sthetic Culture, Spiritual Culture, etc. These are, however, 
but varieties or special forms of those before mentioned, which 
are the ones generally embraced in a scheme of education. 

Physical Culture. — Physical Culture is that which 
relates to the cultivation and development of the physical 
powers. It embraces the culture and attainment of Health, 
Strength, Skill, and Beauty. A full discussion of the subject 
would include a consideration of the conditions, the laws, and 
the methods of securing each one of these objects. 

The first object of physical culture is Health. To a large 
extent man's health is in his own keeping. We can be sick 
or well as we choose. Sickness is the penalty of violating 
physical law. Death, except in old age, is a curse entailed 
upon man by his transgressions. A proper physical culture 
would banish disease and premature death from the land. It 
would increase the average term of life from thirty-three to, 
at least, threescore and ten years. Physical culture seeks to 

(37) 



38 METHODS OF TEACHING. 

ascertain the laws and methods by which these results are 
secured, and to present a sound body as a condition of a 
sound and vigorous intellect. 

The second object of physical culture is StrengiJi.. By cul- 
ture a man can double or treble his natural strength ; and not 
transcend the limits of health. A proper physical culture 
would remove the bodily weakness which we find so prevalent 
in society. It would give muscular fibre and endurance where 
we now find flabbiness and debility. It would give physical 
power to our professional and business men, and enable them 
to endure much more fatigue and to accomplish much more 
than they can at present. It would transform the delicate 
and frail-looking women of to-day, who cannot go upstairs 
without palpitation of the heart, or see a spider without faint- 
ing or shrieking, into women of muscular power and endur- 
ance, such as were the women of Sparta, and as nature 
intended women to be. 

The third object of physical culture is Skill. This is also 
an object worthy of attainment. To use the muscles with 
dexterity, either for pleasure or business, is in itself laudable. 
There is a merit in being a good gymnast, or a good cricketer 
or base ball player. To walk far, run fast, jump a good dis- 
tance, etc., are not unworthy attainments. It is told to the 
credit of Washington that he could leap twenty-four feet on 
a running jump. To possess manual skill and be able to use 
our hands for some useful purpose is especially desirable. 
A knowledge of a use of tools is of great value to every 
person. " Every man his own carpenter" is worth as much 
as "every man his own lawyer." Education should therefore 
aim to cultivate muscular skill and dexterity. 

A fourth object of physical culture is the attainment of 
Beauty. Deformity, like sickness, is the result of violated 
physical law. Had sin never entered Paradise, men would 
be as handsome as Adam, who was no doubt a model in 
physical proportion ; and womcr. would still be as lovely a8 



NATURE OF CULTURE. 39 

Eve, who was, it is believed, the perfection of womanly beauty. 
Let the race keep nature's laws, and we would return toward 
the primitive beauty fashioned by the Divine hand. Art does 
much to restore what we have lost ; but culture is the best 
panacea for ugliness. The best coloring for the cheek is 
pure, rich blood ; the best enamel for the neck and arms is 
the flush of health. Such beauty does not rub off nor come 
and go with the touch of art — " 'T is ingrain ; 't will endure 
wind and weather." 

Intellectual Culture. — Intellectual Culture is that 
which relates to the development and training of the intellect- 
ual powers. The object of intellectual culture is the normal 
growth and highest activity of all the intellectual faculties. 
A full consideration of the subject would present the laws 
and methods by which each susceptibility and power may be 
properly trained and developed. Only a few thoughts will 
be here presented. 

Intellectual Culture aims to cultivate the powers of Obser- 
vation. It enables man to see what is going on around him, 
and to acquire a knowledge of facts and phenomena. It 
makes him sharp-eyed and ready to drink in knowledge at 
every pore. It makes him an original observer of nature and 
society, obtaining his knowledge first hand, instead of de- 
pending on others for it. It thus gives him independence in 
his own ideas of things, and enables him to make contribu- 
tions to the sum of human knowledge. 

Intellectual Culture increases the power of the Memory. 
It gives strength of retention and readiness of recollection. 
It makes man a treasury of knowledge, — a walking li})rary of 
information. It aims to overcome the habit of allowing 
things to fade away from the memory, and trains the mind 
to hold what is worth knowing as a permanent possession. It 
aims to bring the memory up towards the old standard of 
power when men could repeat volumes of manuscript, or "call 
by name the twenty thousand citizens of Athens." 



40 METHODS OF TEACHING. 

Intellectual Culture aims to give activit}^ and direction to 
the power of Imagination. It leads it to delight in ideal 
creations, to enjoy the works of fiction, to wander with pleas- 
ure among the images of poetry, to linger delighted amid the 
romantic events of history, to awaken into activity in view- 
ing the varied beauties of earth, sea, and sky, and to revel 
among the works of art where the pencil of the painter or 
chisel of the sculptor has made a name immortal. It aims 
also to develop the creative power of artistic genius, and to 
stimulate those who have the gift divine to emulate the achieve- 
ments of the masters in poetry, fiction, and fine art. 

Intellectual Culture embraces the training of the power of 
Thought. It aims to make man a thinker, to enable him to 
draw true conclusions from the facts he observes, to exercise 
correct judgment in the afi^airs of life, to investigate and ascer- 
tain the laws of nature and societ}^, to read the truths v/hicli 
God has written upon the pages of earth and sky, to build up 
the sciences and apply their principles to the advancement of 
truth and the improvement of the world. It aims to develop 
the power of thought by which man lifts himself into a higher 
civilization, makes the elements servants of his will to i)ro- 
mote his comfort and happiness, arms himself with the power 
to jDredict the events of the for off" future, and stands at the 
head of created beings, crowned with the triumphs of science 
and philosophy. 

Esthetic Culture, — J]]sthetic Culture embraces the culti- 
vation of the iBsthetic nature. The festhetic nature includes the 
activity of the Reason and the Sensibilities as pertaining to 
the beautiful. The Reason apprehends beauty ; the Sensibili- 
ties admire, appreciate, and enjoy it. ^Esthetic culture seeks 
to develop this nature to the fullest appreciation of the element 
of beauty as found in the works of nature and art, to lift the 
soul upward to the enjoyment of the refined and artistic, to 
refine and elevate the taste, and thus add to man's happiness 
and lend an influence for the growth of his spiritual nature. 



NATURE OF CULTURE. 41 

3Ioral Culture. — Moral Culture embraces the ti'aining of 
the moral nature. The moral nature includes the activity of 
the entire spiritual being; it involves the activity of the 
Intellect, the Sensibilities and the Will. The Reason appre- 
hends the Right and the obligation to do the Right ; the Sensi- 
bilities feel the obligation to act in accordance with an appre- 
hension of obligation ; and the Will puts forth the executive 
volition in obedience to the spiritual imperative. The Es- 
thetic nature consists of idea and feeling; the Moral nature 
consists of idea, feeling, and will. In mathematical phrase- 
ology, the Esthetic nature=the Reason, plus the Sensibilities ; 
the Ethical nature=:the Reason, plus the Sensibilities, plus 
the Will. Moral Culture embraces the full and complete de- 
velopment of this natui'e. 

Heliffioiis Culture. — Religious Culture embraces the train- 
ing and development of the religious nature. The religious 
nature is the highest form of the ethical ; it is the ethical acting 
in relation to the Supreme Being. It implies the consecration 
of all our powers to God, and requires their fullest and highest 
activity. The highest operation of the Reason is Faith ; the 
highest opei'ation of the Sensibilities is Love ; the highest ope- 
ration of the Will is Obedience. The elements of religion, 
therefore, are Faith^ Love, and Obedience] Faith in God and 
salvation ; Love to God and man ; Obedience, the complete sub- 
ordination of the human will to the Divine. Here we reach 
the crowning excellence of man's being, the keystone of the 
spiritual arch. Religious culture thus aims to cultivate faith 
in God, love to God and man, and complete obedience to 
the Divine will. ! ~ — 



CHAPTER yi. 



METHODS OF CULTIVATING EACH FACULTY. 



HAVING attained a knowledge of the nature of the mind 
and the general nature of culture, we are prepared to 
apply these to the training of each faculty of the mind. Only 
a few brief suggestions can be made ; the subject would 
require a volume to ti'eat it with any degree of completeness. 

Perception. — The Perceptive Powers should be cultivated 
in early childhood. This is indicated by Nature, who gives 
active senses to a little child. Teachers have been entirely 
too neglectful of their duty in this respect. Children have 
not been trained to use their eyes and their other senses as 
they should have been. They have been taught to read the 
text-books of the school-room; but, to a large extent, the 
"book of Nature" has been a sealed volume to them. 

The Perceptive Powers may be cultivated by training chil- 
dren to a habit of observation. The following suggestions 
will indicate to teachers the method of cultivating the per- 
ceptive faculty : 

1. To cultivate the Perceptive Powers^ require pupils to 
observe things for themselves. Bring objects into the school- 
ro6m for them to see and examine. Send them out into the 
fields and woods to gather facts for themselves. Teach them 
to read the book of nature as well as the books of the school- 
room. 

2. To cultivate the Perceptive Powers^ require pupils to 
describe objects. In order to describe an object, it must be 
very closely observed. The attempt to describe will lead 
pupils to see the necessity of examining an object with atten- 
tion, and will give quickness and accuracy to the perceptive 
powers. ^^2^ 



I 



CULTIVATING EACH FACULTY. 43 

3. To cultivate the Perceptive Powers, train pupils upon a 
well graded system of object-lessons. Give the pupils lessons 
on form, color, size, etc., and they will learn to notice these 
elements in the objects that they see. The sense of vision 
will thus become sharp, delicate, and accurate. 

4. Require pupils to draw outlines or sketches of objects. 
In order to draw an outline of an object it is necessary to 
examine it very minutely. The practice of drawing will 
thus cultivate the habit of close and minute observation. 

Such exercises will train pupils to the habit of using their 
perceptive powers, and habit is nearly everything in educa- 
tion. Teachers should also impress upon the minds of their 
pupils the importance of using their eyes, and not going 
through the world blind to its most interesting facts. 

The Memory. — The Memory should be carefully trained 
in youth, so that it may firmly hold the knowledge acquired 
and readily recall it. Minds differ in natural power of mem- 
oi-y, but much can be done to strengthen a weak or quicken a 
sluggish memory. A neglect of the proper use of this faculty 
leads to habits which weaken it, and make it slow to acquire 
and unreliable in recalling its knowledge. 

The following suggestions will indicate to the teacher how 
he may cultivate the memory of his pupils : 

1. To cultivate the Memory, require pujnls to attend closely 
to whatever subject they are considering. Attention is a 
necessary condition of remembering. A heedless mind soon 
forgets what it sees, hears, or reads. The mind must be con- 
centrated upon the object of thought that it may be indelibly 
impressed upon the memory. 

2. To cultivate the Memory^ lead pupils to feel an interest 
in what you wish them to remember. An interested mind is 
open to receive the deepest impression. An incident which 
excites the mind is never forgotten. A pupil who takes 
delight in what he is learning will have little difficulty in 
acquiring it, and will retain it permanently. 



M METHODS OF TEACHING. 

3. To cultivate the Memory^ we should require a frequent 
revieio or repetition of that which the pupil has learned. 
Repetition seems to fix a subject more firmly in the memory-. 
It acts like the die on a waxen tablet ; every repetition seems 
to make the impression more durable. The subject most fre- 
quently recited is the most readil}'' recalled, and remains the 
longest in the memory. 

4. To cultivate the Memory^ loe should require pujnls to 
commit many extracts of prose and poetry. This will fix 
words and forms of expression in the mind, and cultivate a 
memor}^ for language. Practice of this kind will give great 
facility in committing, while a neglect of it will so enfeeble 
the memor}'^ that it will be almost impossible to commit any- 
thing. 

5. To cultivate the 3Iemory^ ice should lead the pujnls to 
connect their knoicledge by the laws of association. This is 
the way in which the memory naturall}'^ acts, and in which it 
acts with the most readiness and accuracy. The pupil should 
associate similar facts in geography, events of the same date 
in history, or those related as cause and etfect. Such a habit 
will give a strong and reliable memory. 

The Imagination. — The Imagination of children should 
be carefully cultivated. This faculty is usually very active 
in childhood, and needs guiding and refining. When it is 
sluggish, it should be excited and aroused into activit}' ; when 
it is too active, it should be restrained and directed. The 
judicious training of this faculty will be of great value to 
the pupil. It will be a source of pure and refined pleasure, 
and will exert an elevating influence on the character. 

1. The Imagination may be cultivated by observing beauti- 
ful, grand, and picturesque scenery. The spreading land- 
scape, the flowing river, the wide extended ocean, the arching 
sky, out of whose deep blue the golden stars are shining, the 
moon in her beauty and the sun in his splendor — all these 
tend to give activitv and culture to the imagination. 



i 



CULTIVATIXG EACH FACULTY. 45 

2. The Imagination may he cultivated hy filling the memory 
xcith beautiful pictures of natural scenery. The beautiful 
objects we have seen should be brought before the mind as 
pictures upon which it delights to look. Each mind may 
thus be a gallery where pictures of beauty hang upon the 
walls of memory, exciting the imagination to activity and 
furnishing it with pure and lofty ideals. 

3. The Imagination may he cultivated hy reading poetry, 
fiction, and other imaginative comjwsitions. Such produc- 
tions are the embodiments of the imaginings of others, and 
awaken our own imaginations into activity. The figures of 
the poet, the characters and incidents of fiction, linger in the 
memory and stimulate us to create for ourselves such images 
of beauty and incidents of life. 

4. The Imagination may he cultivated hy hearing music, 
visiting galleries of painting, statuary, etc. Here we have 
the embodiment of imaginative beauty in color and form, 
which pleases and excites the fancy. That which was once in 
the imagination of the creator awakens a similar activity in 
the mind of the beholder. There is thus cultivated a pure 
and refined taste, and a natural and lively activity -of the 
Imagination. 

5. The Imagination may be cultivated hy creating imagin- 
ary scenes, incidents, etc. The creative power of the Imag- 
ination is its highest office, and such exercise gives it the 
highest culture. The pupils can be led to create and describe 
ideal landscapes or incidents of human action. They may be 
required to write and relate imaginary or fictitious events, as 
allegories, parables, novelettes, etc. Poetical composition 
and the creating of figures of rhetoric afford valuable culture 
in this respect. 

The Understanding. — The Understanding 'of children 
should also be carefully trained. Pupils should be taught to 
think, as well as to see and remember. Care should be taken 
that the memory be not required to do that which the under- 



46 METHODS OF TEACHING. 

standing of the child should perform. Perhaps the greatest 
mistake of school work is made just at this point. There is 
often too much cramming, and not enough thinking in our 
schools. 

1. The Understanding may he cultivated by the study of 
thought studies, as Mental Arithmetic, Written Arithmetic, 
Grammar, Geometry, etc. These studies require pupils to 
think, and pupils learn to think by thinking. Care should be 
taken that the pupils study with the understanding and not 
merely with the memory. 

2. The Understanding may be cultivated by working out 
original problems, parsing and analyzing sentences, etc. 
These exercises require the pupils to employ the power of 
original thought. They lead the mind to compare, and the 
process of comparison lies at the foundation of thinking. 
The judgment must be exercised to apply the principles and 
rules, and to see the relation of the conditions of the problem 
or the elements of the sentence. 

3. The Understanding may be cultivated by writing compo- 
sitions and trying to think out and express something new. 
Such exercises bring into activity the inventive powers of the 
mind. They require the pupil to elaborate his knowledge, to 
work it up into new forms, to think out something new for 
himself. Writing original compositions is thus a most excel- 
lent exercise for the cultivation of thought-power. 

4. The Understanding may be cultivated by the study of the 
mathematical and physical sciences. The three best studies 
to develop the power of thought are Mental Arithmetic, for 
the young student ; Geometr}"^, for students from fourteen to 
eighteen years ; and Mental Philosophy and Logic, from 
eighteen years and upward. For inductive tliought, the nat- 
iiral science^ should be studied ; as Botany and Natural 
Philosophy. The former teaches pupils to generalize and clas- 
sify ; the latter to investigate the causes and laws of things. 

5. The Understanding may he cultivated by reading the 



CULTIVATING EACH FACULTY. 47 

ivorks of the great thinkers. To follow thought, as expressed 
in language, will stimulate to thinking. By reading the works 
of Plato, Aristotle, Bacon, Hamilton, etc., the mind becomes 
familiar with great thoughts and is aroused to think for itself. 

6. The Understanding may be cultivated by thinking. We 
learn to think by thinking, thinking^ thinking. 

Attention. — The power of Attention should be carefully 
trained in childhood. It is one of the most important of the 
mental powers, for upon its activity depends the efficiency of 
each one of the specific faculties. Mental power is, to a large 
extent, the power of attention ; and genius has been defined as 
" nothing but continued attention." 

The following suggestions will indicate to the teacher the 
methods by which the power of attention can be cultivated : 

1. Have pupils observe objects closely. 

2. Reqviire them always to study with close attention. 

3. Read long sentences and have pupils write them. 

4. Read quite long combinations in mental arithmetic, and 
have pupils repeat them. 

5. Mathematical studies are especially valuable in cultivat- 
ing the power of attention. 

The following suggestions are made to aid a teacher in 
securing the attention of his pupils : 

1. Manifest an interest in the subject you are teaching. 

2. Be clear in your thought, and ready in your expression. 

3. Speak in a natural tone, with variety and flexibility of 
voice. 

4. Let the position before the class be usually a standing 
one. 

5. Teach without a book, as far as possible. 

6. Assign subjects promiscuously, when necessary. 

T. Use the concrete method of instruction, when possible. 

8. Yary your methods, as variety is attractive to children. 

9. Determine to secure the attention at all hazards. 



CHAPTER VII. 



THE NATURE OF KNOWLEDGE. 

IN order to give instruction skillfully, a teacher should have 
an idea of the general nature of the different branches of 
knowledge and their relations to one another. He should see 
clearly the elements of which the different branches are com- 
posed, the relation of these elements to the human mind, 
and the manner in which the sciences are developed. We 
shall, thei-efore, present a brief discussion of the Natui-e of 
Knowledge. 

Common and Scientific, — All knowledge may be embraced 
under two general divisions •, Common Knowledge and Scien- 
tific Knowledge. Common Knowledge consists of unsystem- 
atized facts, ideas, and truths. It is a knowledge possessed by 
the common people, and is the basis of Scientific Knowledge. 
Scientific Knowledge consists of facts, ideas, and truths, sys- 
tematized and expressed in the form of laws and principles. 
It enables man to interpret the facts and phenomena of nature, 
to see the great laws by which the universe is governed, and 
to previse and predict the events of the future. 

General Division of Science. — Scientific knowledge has 
been divided into two general branches; the Empirical 
Sciences and the Rational Sciences. This classification is 
based upon the relation of their subject matter and methods 
of development to the human mind. 

The Empirical Sciences are those which are founded on the 
knowledge derived through the senses: they are developed 
by Generalization, Classification, and Inductive Reasoning. 
Geography, Botany, and Natural Philosophy are examples of 
the empirical sciences. The facts of these sciences are given 

(48) 



THE NATURE OF KNOWLEDGE. 49 

by Perception: these facts are classified by Generalization, 
and their laws and causes are derived by Induction. 

The Rational Sciences are those which are founded on the 
knowledge given by Intuition or the Reason : they are devel- 
oped by Deductive Reasoning. Arithmetic, Geometry, Logic, 
etc., are examples of the rational sciences. The fundamental 
ideas and axiomatic truths of these sciences are given b}' 
Intuition, and their derived truths are obtained by Deduction. 

Schemes of Classification. — There have been many at- 
tempts made to classify knowledge ; but no scheme of classi- 
fication has yet been presented which has been universally 
accepted. Comte, the celebrated positive philosopher, classi- 
fies the sciences with respect to the mattei' of which they are 
composed. His classification is as follows : Mathematics, 
Astronomy, Physics, Chemistry, Physiolog}^, and Social 
Ph3^sics. Dr. Hill classifies the branches according to the 
order of their development. His classification is Mathesis, 
Ph^'sics, Histor}^ Psycholog}^ and Theology. Dr. Wicker- 
sham groups the sciences together under the following heads : 
The Elements of Knowledge, Language, The Formal Sciences, 
The Empirical Sciences, The Rational Sciences, The Histori- 
cal Sciences, and The Arts. 

Author's Classification. — Without discussing these sev- 
eral schemes of classification, we shall present one which we 
think best suited to the training of young teachers. Knowl- 
edge may be classified into seven principal divisions: 1. Lan- 
guage, 2. Mathematics, 3. Physics, 4. History, 5. The Arts, 
6. Psychology, 7. Theology. This classification is simple, 
and has the advantage of employing the names of the branches 
as generally used in our schools. 

These general branches and their subdivisions are not 
always entirely distinct from one another. They often over- 
lap one another and intrude upon one another's territory. It 
is impossible to draw a line, in every case, marking just where 
one branch ends and another begins. This is true with 
a 



50 METHODS OF TEACHING. 

respect to every classification that has been attempted. The 
scheme here presented seems more satisfactory, for the pur- 
pose of teaching, than any that we have met, 

Liangiiage. — Language is the instrument of thought and 
the medium of expression. The tenn is derived from lingua^ 
the tongue. Primarily, Language is the means of communi- 
cating knowledge : it enables one mind to transfer its thought 
to another mind. It is also found that language is the means 
by which we think, as well as the medium by which we com- 
municate our thoughts. We cannot think to any great 
extent, if at all, without language; and the more perfect our 
language the more powerful our thought — as in algebra, arith- 
metic, etc. We therefore embrace these two uses of language 
in our definition, and define it to be the instrument of thought 
and the medium of expression. 

3Iathetnatics Mathematics is the science of Quantity. 

The term is derived from mathemafike, meaning science. It 
investigates the relations of quantity, and unfolds the truths 
and principles belonging to it. It is based on intuitive ideas 
and truths, and developed by deductive reasoning. The three 
principal branches are Arithmetic, Geometrj^, and Algebra. 
Arithmetic is the science of Number ; Geometry is the science 
of Space ; Algebra is a general method of investigating all 
kinds of quantity by means of symbols. 

Physics. — Physics is the science of the material .world. 
The term is derived from phusis, nature. It consists of facts 
and phenomena, and the laws and principles which control 
them. It begins with the observation of facts, compares and 
classifies them, and ascertains the causes which give rise to 
them and the laws which control them. The principal 
branches ai'e Geography, Natural History, Natural Philoso- 
phy, Astronomy, Chemistry, Geology, etc. 

Geography treats of the facts relating to the surface of the 
earth, classifies them, and investigates their causes and the 
laws which govern them. Natural History treats of the three 



THE NATURE OF KNOWLEDGE. 51 

kingdoms of nature, — the mineral, the vegetable, and the ani- 
mal, — ascertaining the nature, structure, etc., of the indi- 
vidual objects, and classif3dng them. It includes Mineralogy, 
Botany, and Zoology. Natural Philosophy treats of the facts 
and phenomena of nature, and ascertains their causes and the 
laws which govern them. It includes Mechanics, Optics, 
Acoustics, etc. Astronomy treats of the facts and truths 
relating to the heavenly bodies. Chemistry treats of the na- 
ture and properties of the elements of bodies. Geology treats 
of the origin, development, and structure of the earth. 

History. — History is a systematic description of the past 
acts and condition of mankind. It embraces the Facts of 
History and the Philosophy of History. The Facts of History 
embrace the events that have occurred in the life of individu- 
als and nations. The Philosophy of History endeavors to 
ascertain the causes which have contributed to produce the 
different changes in society and nations, and thus to predict 
the future condition of the race. In other words, it endeavors 
" to solve the problem of man's condition and destiny." 

Art. — Art is the application of knowledge or power to effect 
some desired object. It is the outgrowth of practice, and may 
be defined as practice guided by principle. The Arts are 
divided into two general classes ; the Fine Arts and the Use- 
ful Arts. The object of the Useful Arts is the attainment of 
the end of utility; the object of the Fine Arts is the attain- 
ment of the end of beauty. These two, though primarily dis- 
tinguished, are often combined in the same production ; as in 
the manufacture of glass and pottery ware, in architecture, 
engraving, etc. 

Psychology. — Psychology is the science of the human 
mind. The term is derived from psj/c/ie, the soul. It is 
sometimes divided into Empii-ical Psychology and Rational 
Psychology. Empirical Psychology treats of the nature of 
the mind as revealed in the experience of' consciousness. 
Rational Psychology treats of the nature of the mind as de- 
termined ]iy the necessary principles given hy the Reason. 



62 



METHODS OF TEACHING. 



Theologif' — Theology is the science which treats of God. 
The term is from Theos, God, and logos, a discourse. It has 
been divided into Natural Theolog}'^ and Revealed Theology. 
Natural Theology endeavors to ascertain the nature of God 
through his works, by the light of philosophy and reason. 
Uevealed Theology seeks a knowledge of the Divine Being 
through his revealed word. 

Other Distinctions. — It is often convenient to speak of 
the Inductive and the Deductive Sciences. The former in- 
clude all those branches of knowledge which begin in facts 
and are developed by generalization and inductive reasoning ; 
as geography, botany, natural philosoph}^ etc. The latter 
include all those branches of knowledge which begin in ideas, 
and are developed by the process of deductive reasoning ; as 
arithmetic, geometry, etc. A division of the Rational Scien- 
ces is often made, called the Formal Science^ The Formal 
Sciences may be defined to be those sciences which treat of the 
necessary forms in which truth presents itself. They include 
Mathematics and Logic ; Mathematics treating of the form in 
which quantity is presented, and Logic of the form in which 
thought presents itself. 



I 



CHAPTER YIII. 

THE FORMS OF INSTRUCTION. 

INSTRUCTION, as primarily defined, is the imparting of 
knowledge to the mind. It is the art of transferring 
knowledge from one mind to another. By it we are enabled 
to build up in the mind of the learner a knowledge of the 
sciences, as an architect erects a building. Under the direc- 
tion of a teacher, a science is developed in the mind in symme- 
try and beauty as a temple is erected under the guiding genius 
of a skillful architect. 

Knowledge may be presented to the mind in different ways ; 
these different ways we call Forms of Instruction. There is 
a certain order in which knowledge should be presented to 
the mind ; this order we call the Order of Instruction. There 
are certain laws which should guide a teacher in imparting 
instruction ; these laws we call the Principles of Instruction. 
In discussing the Nature of Instruction we shall speak of the 
Forms of Instruction, the Order of Instruction, and the Prin- 
ciples of Instruction. 

The Forms of Instruction are the various ways in which 
we may impart knowledge. The principal Forms of Instruc- 
tion are the Analytic ?inA. Synthetic , the Concrete and Abstract, 
the Inductive and Deductive^ the Theoretical and Practical. 
We will define and illustrate each one of these forms. 

Analytic and Synthetic. — Analytic Instruction is that 
form of teaching which proceeds from wholes to parts. Thus, 
if I take a watch and separate it into parts, and teach the 
name and office of each part as I take it to pieces, the process is 
anal3-tic. So in grammar, if I begin with the sentence and 
separate it into its parts, I am using the analytic process. If 
in geography we begin with the globe as a whole, and separate 



54 METHODS OF TEACHING. 

it into land and water, and come down from continents and 
oceans to the smaller divisions, the process is analytic. 

Synthetic Instruction is that form of instruction which pro- 
ceeds from parts to wholes. Thus, if we take the parts of a 
watch as separated, and putting them together, teach the name 
and use of each part, we are teaching synthetically. If in 
grammar we begin with the words as parts of speech, and put 
them together to form sentences, we are teaching by the syn- 
thetic method. So if we begin with the geography of the 
school grounds, go out to that of the township, the county, 
and the state, and thus at last cover the entire surface of the 
earth, the method is synthetic. 

Concrete and Abstract. — Concrete Instruction is that 
form of teaching which employs objects and illustrations. 
Thus, object lessons, or the use of pictures and diagrams, are 
exami:)les of concrete instruction. In Arithmetic, the teaching 
of the fundamental operations by means of the numeral 
frame, of fractions by means of illustrations, of denominate 
numbers by means of the actual measures, of banking by 
establishing a bank in the school, are examples of concrete 
instruction. Grammar taught from language, rather than 
from the rules of the text-book, is also concrete teaching. 

Abstract Instruction is that form of teaching which does 
not employ objects and illustrations. In Arithmetic, counting, 
addition, etc., taught without any objects or illustrations, 
denominate numbers by merely repeating the tables, per- 
centage by the definitions and rules without illustrating the 
actual business transactions, etc., are examples of abstract 
instruction. Grammar taught from the definitions of the 
text-books, instead of from language in which we find the 
principles embodied, is abstract instruction. Teaching Geog- 
raphy from the book, rather than from natural objects, is an 
example of abstract instruction. 

Inductive and Deductive. — Inductive Instruction is that 
form of teaching which proceeds from particulars to generals. 



THE FORMS OF INSTRUCTION. 55 

The leading of pupils by appropriate questions and examples 
to the apprehension of an idea or principle before it is stated, 
is a process of inductive teaching. Thus, in Arithmetic^ if by 
presenting particular examples we lead the pupil to see the 
principle or rule before stating it, we teach inductively. If 
in Geometr^^, by apjDropriate examples, we lead the pupil to 
a geometrical idea or principle, and then require him to 
express it, we are teaching inductively. In Grammar, teach- 
ing inductively, we would lead a pupil to the idea of a part of 
speech before we named and defined it ; or lead him, as we 
often can, to the name of a part of speech, without his learning 
it from a book or the teacher. 

Deductive Instruction is that form of teaching which pro- 
ceeds from generals to particulars. If we first state the gen- 
eral principle and then lead to the particular applications of 
it, we are teaching deductively. Thus, in Arithmetic, we va^y 
teach the pupil the principles of fractions, and then have him 
apply them ; or in Grammar we may teach the words of a 
definition, and then illustrate its meaning : in both cases we 
are teaching deductively. Deriving ideas from definitions, 
methods from principles, particular methods from general 
laws, are all deductive methods of procedure. 

The Inductive and Deductive methods may be distinguished 
even in stating definitions. Definitions may be stated either 
in an inductive or a deductive form. If we begin with ■ the 
term to be defined and pass to its explanation, the form is 
deductive ; but if we begin by giving the idea, and end by 
naming the term, the form is inductive. Thus " Addition is 
the process of finding the sum of two or more numbers," is 
in the deductive form ; and " The process of finding the sum 
of two or more numbers is called Addition," is in the induc- 
tive form of stating a definition. 

Theoretical mid Practical. — Theoretical Instruction is 
that form of teaching which deals principally with the laws 
and principles of a subject. Teaching the theory of arithmetic 



56 METHODS OF TEACHING. 

without making an application of it to practical problems, is 
an example of theoretical teaching. The so-called practical 
problems of arithmetic, are sometimes purely theoretical, 
never occurring in actual life. Teaching the definitions and 
principles of grammar without applying them — a fault not 
uncommon — is also an illustration of theoretical instruction. 
The teaching of geometry without any application of its prin- 
ciples to practical problems, a very common fault, is also an 
example of theoretical instruction. 

Practical Instruction is that form of teaching which deals 
principally with the application of the laws and principles of 
a subject. When pupils are required to apply the principles 
of arithmetic to actual pro-blems, and the students of grammar 
are taught to use the principles of language in their own 
speech and writing, we have an illustration of practical teach- 
ing. To open a counting-house in the school-room and show 
by actual transactions what the business problems of arith- 
metic mean, is practical instruction. The application of the 
principles of geometry to actual problems that ma}'^ occur to 
a business man, and also to surveying and engineering, fur- 
nishes an example of practical instruction. 

Application, — Several of these forms may be used in teach- 
ing the same subject ; and sometimes one form is preferable 
and sometimes another. The concrete and inductive forms 
should be used with children ; the abstract and deductive 
forms are more suitable to older pupils. Anal3'sis and syn- 
thesis are often employed in teaching the same subject; 
though, as a rule, the analytic form should precede the syn- 
thetic. All instruction should be practical, though at certain 
stages the abstract element may predominate. It is not our 
purpose to point out the use of these forms here, but merely 
to make the pupil fomiliar with the forms themselves. Their 
use and special application will be indicated in the chapter on 
the Principles of Instruction, and in the methods of teaching 
the particular branches of study. 



CHAPTER IX. 

THE ORDER OF INSTRUCTION". 

THE school-time of life has been divided into four periods ; 
Infancy, Childhood, Youth, and Manhood. Infancy em- 
braces the period from the birth of the child to the age of five 
years ; Childhood, the period from five to ten years ; Youth, 
the period from ten to sixteen years ; and Manhood, the period 
from sixteen to twenty-one years. . 

These are not definitely fixed periods, as some persons 
mature very much earlier than others. Girls from twelve to 
sixteen years of age are usually much more mature than boys 
of the same age. The distinctions are sufficiently definite, 
however, for the purpose in view. The inquiry is, What is an 
appropriate course of study for each one of these periods ? 
How much of the several branches — Language, Mathematics, 
Physics, History, the Arts, etc., shall be taught in each one 
of these periods ? 

Several writers treat of this subject under the head of a 
Graded Course of Studj^, in which they attempt to fix the kind 
and amount of knowledge suitable for the various grades of a 
public school. Dr. Hill, who has a very complete discussion 
of the subject, divides the school time into five distinct 
grades ; the first, or Sub-primary school, from five to eight ; 
the second or Primary school, from eight to eleven; the third, 
or Grammar school, from eleven to fourteen ; the fourth, or 
High school, from fourteen to seventeen ; and the fifth, or 
College period, from seventeen to twenty-one. This is practi- 
cal ; but as grades in diiferent places vary, it has been thought 
best to discuss the subject in general under the four heads 
named, as is done by Dr. Wickersham in his Ilethods of In- 
3:^ (57) 



68 



METHODS OF TEACHING. 



struction. Any teacher who understands the order presented 
will have no difficulty in arranging the studies of a graded 
school. 

Infancy' — During this period a child learns to talk. It 
may also learn a few written words, and the letters of the 
alphabet. In Mathematics, it may learn some of the figures 
of geometiy, to count as far as twentj^-five or fiftj', and per- 
haps to add and subtract a few of the smaller numbers with 
objects. It will acquire a large number of facts in botany and 
zoology, and also many of the elementary facts and phenomena 
of natural philosophy. It may also become familiar with a 
few fticts of history, learn to sing little songs, and to use a 
pencil and draw a little. This instruction should be giA^en at 
home or in a kindergarten. 

Childhood. — During childhood, the child should learn to 
read, to spell, to pronounce correctly, and to express itself 
with considerable correctness and facility, both in speaking 
and in writing. It should receive a S3'Stematic course of in- 
struction in Language Lessons, including orthography, the 
construction of sentences, the use of capitals, punctuation 
marks, etc. There should not, however, be any formal in- 
struction in Grammar. If circumstances will permit, the child 
may learn to speak one or two modern languages, and even 
elementary instruction in Latin could be given. 

Instruction in Arithmetic should embrace numeration and 
notation, — the naming, writing, and reading of numbers ; 
the fundamental operations of addition, subtraction, multipli- 
cation, and division ; the elements of common fractions, 
decimals, and denominate numbers. In Geometry, he shauld 
become familiar with all the ordinar}^ figures, both plane and 
solid ; learn to construct and point out their diflTerent parts 
and elements ; and perhaps learn a few of the elementary 
truths of the science. 

In the facts of the Physical Sciences, his course should be 
quite extensive. He should become familiar with the leading 



THE ORDER OF INSTRUCTION. 59 

facts of descriptive geography, and be able to locate the prin- 
cipal countries, cities, rivers, mountains, etc., of the world. 
In Botany, he should become familiar with the ordinary trees 
of his neighborhood, the principal flowers of the garden and 
meadows, be able to name many of the forms of leaves 
and corollas, etc. He should also learn the names of the 
principal animals, domestic and wild ; many of the ordinary 
insects, and some of the more common fishes. He should also 
learn the common minerals of the neighborhood ; as quartz, 
limestone, sandstone, granite, etc. Many of the simple facts 
and phenomena of Natural Philosophy, and the causes of the 
same, may also be learned, and some of the simpler experi- 
ments of the science may be presented to him. 

During this period a child can learn, by oral instruction, 
many of the leading facts of the History of the world, and of 
his own country. He is able also to read works on biography 
and histor}', if written in a simple and interesting style, and 
should be encouraged to do so. In the Arts, he should be 
taught to write, to draw, and to sing ; and if he has any 
musical taste, may begin to learn to play some instrument. 
Boys should learn the use of a knife and other tools, and 
girls the use of the needle, scissors, etc. 

Youth. — During the period of j^outh, the pupil should con- 
tinue the study of Language, increasing his vocabulary and 
acquiring skill in the use of his mother tongue. He should 
have a careful drill in orthography, pronunciation, and read- 
ing. He should also begin the study of grammar and the 
elements, of rhetoric, learn to use the dictionary, and have 
constant exercises in composition writing. He should be 
required to read, commit, and recite choice extracts of prose 
and poetry for the cultivation of a literar}^ taste. He should 
also begin the study of Latin and Greek, and perhaps one or 
two foreign languages. An extensive course of reading in 
poetry and prose would also be of advantage. 

In Mathematics, he should go through an ordinary text- 



60 METHODS OF TEACHING. 

book on mental and written arithmetic ; begin and in manj'' 
cases complete an elementary Avork on algebra ; and if he has 
had a good oppoi'tnnity for mathematical study, should com- 
plete an elementary text-book on geometry. Of the Physi- 
cal Sciences, he should continue his course in descriptive 
geography, and also study physiology, botany, natural philoso- 
phy, astronomy, and physical geography. During this period 
he can complete the elements of these branches as they are 
presented in the ordinary elementary text-books. Some of 
the elements of zoology and mineralogy should also be in- 
cluded in the course of studies arranged for pupils from ten to 
sixteen years of age. 

During this period he may complete the ordinary text-book 
on the history of his own country, and even a small text-book 
on general history. He should also read such works as the 
RoUo Books, Abbott's Histories, and other works of biogra- 
raphy, travels, voyages, and explorations. The historical 
stories of Miss Yonge and Miss Strickland are especially 
recommended to pupils of ten or twelve years of age. 

He should learn, during this period, to write a good hand, 
to draw with considerable skill, to read music by note, to sing, 
and if he has musical talent, to play one or two instruments. 
If there is special talent for the mechanic or fine arts, an 
opportunit}^ should be afforded for its culture. 

Some of the elements of Mental and Moral Philosophy 
might be learned during this period, but it is thought that any 
formal study of these branches should be usually postponed 
until afteii^the age of sixteen. 

Manhood . — During this period the Language studies of the 
previous period should be continued into their higher depart- 
ments ; in addition to which there should be a thorough course 
in Rhetoric, General Literatui'e, Philology, etc. There 
should also be an extensive course of general reading of the 
poets and prose writers, and a close and careful study of some 
of them as models of style and expression. There should 



THE ORDER OF INSTRUCTION. 61 

also be much practice in composition, and the pupil should 
become a good writer and speaker. 

The Mathematical studies of this period should include 
higher arithmetic, higher algebra, higher geometry, trigonom- 
etry and surveying, analytical geometry, differential and 
integral calculus, and the philosophy of mathematics. If 
there is time, some of the recently developed branches of the 
science may also be studied ; and the pupil should be encour- 
aged to push his investigations beyond any of the ordinary'' 
text-books on the subject. 

The course in Natural Science should include a higher 
course in Natural Philosophy, embracing mechanics, optics, 
acoustics, etc. ; a course in theoretical and practical Astron- 
omy ; a full course in Chemistry, Anatomy, and Physiology; 
and, if possible, quite a thorough course in Natural History. 
The student should also begin the investigation of the facts 
and phenomena of the material world for himself. 

The course in History should include the reading and study 
of a complete history of one's own country, a complete course 
in general history, a careful reading of the detailed history of 
England, France, Germany, Spain, etc., a study of the works 
on the* philosophy of history, as Guizot, Buckle, Draper, etc. 
The effort should be to fix permanently in the mind all the 
great and leading events of history, and to learn the causes 
which have contributed to the rise and fall of empires and 
nations, and thus to learn the laws which control the growth 
of civilization. 

The course in the Arts may or maj- not be continued, ac- 
cording to the taste and circumstances of the pupil. When 
there is musical taste, it may include the culture of the voice, 
singing, instrumental music, thorough-bass, musical composi- 
tion, etc. When there is taste in drawing, it may include 
sketching from nature, perspective drawing, painting, etc., 
and the history and philosophy of art. A thorough coiirse in 
Architecture and Landscape Gardening will also be of inter- 
est and value to the student if there are taste and time for it. 



62 METHODS OF TEACHING. 

The student is now prepared for what are called the Meta- 
physical studies. During this period, he should take a course 
in Mental Philosophy, Moral Philosophy, Logic, Political 
Economy, Esthetics, International Law, and the Evidences 
of Natural and Revealed Religion. The works of the great 
thinkers, Plato, Aristotle, Bacon, Locke, Kant, Hegel, Fichte, 
Hamilton, and the writers on the relation of modern science 
to philosophy and religion, may be studied. Many of these 
studies, however, can be merely begun at the age of twentj'- 
one, and should be continued through life. 

The course suggested will be found to be just a little in 
advance of the capacity of the average boy and girl, as we 
find them in our families and schools ; but if the pupil have a 
careful systematic training from the beginning, he will be 
prepared for the studies named. The object is to present an 
ideal of what the course should be, and of what we should aim 
to make it. 



CHAPTER X. 

THE PRINCIPLES OF INSTRUCTION. 

THE Principles of Instruction are the laws which guidr? 
the teacher in imparting instrqction. These principle.^ 
are derived from three distinct sources ; the Nature of th<; 
Mind, the Nature of Knowledge, and the Nature of Iti- 
struction. The principles derived from the nature of the 
mind have reference to the proper culture of the ment-'J 
faculties ; those derived from the nature of knowledge have 
reference to the order in which knowledge shall be presented 
to the mind ; and those derived from the nature of instruction 
have reference to the manner in which knowledge shall be 
taught. We shall present ten principles of each class, which 
may be called the Teacher^s Decalogue. 

Principles^Derived from the Nature of Mind. 

The following ten principles are derived from the nature of 
the mind, and indicate the laws which should govern the 
teacher in imparting instruction so that the mind may be 
properly trained and developed : 

1. In education culture is loorth more than knowledge. Cul- 
ture gives the power to acquire knowledge, and this is more 
valuable to the pupil than the knowledge he has already 
acquired. Culture also gives one the power to originate 
knowledge, to invent new ideas and thoughts. Without cul- 
ture the mind is a mere receptacle of ideas and thoughts ; with 
it the mind is an active energy that can transform its knowl- 
edge into new products. Knowledge makes a learned man ; 
culture makes a wise man ; and wisdom is better than learning. 
This primary object of teaching should ncA^er be forgotten. 

(63) 



64 METHODS OF TEACHING. 

The teacher should carry in his mind a clear conception of the 
faculties of his pupils, and keep constantly before him the 
thought whether his work is adapted to the growth and culture 
of these faculties. He should know the relation of each branch 
of study to the minds of his pupils, see clearly what faculties 
are brought into activity by it, and be sure that his work is 
giving, not merely knowledge, but intellectual power. In 
other words, he should measure his work, not merely b}^ the 
knowledge he is imparting, but by the mental power he is cul- 
tivating. The neglect of this duty has warped and stunted 
many a young mind. 

2. Exercise is the great law of culture. This law is univer- 
sal, applying to both mind and matter. A muscle grows strong 
by exercise. The arm of the blacksmith and the leg of the 
pedestrian acquire size and power by use. So every faculty 
of the mind is developed by its proper use and exercise. The- 
power of perception grows by perceiving, the power of mem- 
ory by remembering, the power of thought by thinking, etc. 
Hang the arm in a sling and the muscle becomes flabby and 
almost powerless ; let the mind remain inactive and it acquires 
a mental £abbiness that unfits it for any severe or prolonged 
activity. An idle mind loses its tone and strength, like an 
unused arm ; the mental powers go to rust through idleness 
and inaction. 

3. The teacher should aim to give careful culture 'to the 
perceptive powers of the child. The perceptive powers are 
the most active in childhood. Mental activity begins in the 
senses. A little child almost lives in its eyes and ears and 
fingers ; it delights to see and hear and feel. Its eyes are 
sharp, its ears are quick, and its fingers so busy as to be con- 
tinually in what people call " mischief." The teacher should 
direct this activity', and give the child food for the senses. 
He should provide objects for its instruction, and give it facts 
to satisfy this craving mental appetite, rather than attempt to 
feed it upon abstract ideas and thoughts for which it has no 
taste or capacit}'. 



THE PRINCIPLES OF INSTRUCTION. 65 

4. The teacher should aim to furnish the memory of the 
child with facts and words. The memory of children is es- 
pecially strong for facts and words. Every object of nature 
coTnes through the senses with such a freshness to the mind 
that it stamps itself indelibly on the memory. Facts seem to 
stick as naturally to the young mind, as burrs to the dress. 
Its memory for words is no less remarkable than its memory of 
things, A new word, once heard, is usually a permanent pos- 
session. A child will learn to speak three or four languages 
in a year, if it has the opportunity of doing so. The teacher 
should remember these facts, and conform his work to them. 
He should give the child an opportunity to furnish its mind 
with the facts of nature and science, and also to add to its 
stock of words and acquire a rich and copious vocabulary. 

5. The memory should he trained to operate by the laws of 
association and suggestion. The mind in retaining and recall- 
ing knowledge works in accordance with a certain law of 
mental operation. It ties its facts together by the thread of 
association, or arranges them in clusters like the grapes of a 
bunch. This tendency is called the Law of Association. The 
principal laws of association are the law of Similars, the law 
of Contrast, the law of Cause and Effect, and the law of Coyi- 
tiguity in Time and Place. The teacher should understand 
these laws and require the pupil to link his knowledge together 
b}'^ means of them. In geography he should have pupils asso- 
ciate similar facts in respect to cities, states, etc.; in history 
he should require them to make use of the law of contiguit}'' 
in time and place, and lead them to associate events as related 
b}^ cause and effect. A.11 the knowledge taught should be so 
systematized that it may be readil}'^ recalled by the law of 
logical or topical relations. 

6. The power of forming ideal creations should be carefully 
cultivated. The faculty of ideal creation is the Imagination. 
This power is awakened into action through the medium of 
perception. The facts of the senses touch the fancy, and 



66 METHODS OF TEACHING. 

arouse it into activity. The forms and colors of nature, the 
arching sky and the spreading landscape, linger in the mem- 
or}^ as forms of beauty, and excite the imagination to modify 
and create such forms for itself. This tendency is sometimes 
so strong, that fact and fancy become so interwoven in the 
mind of a child that it is difficult to discriminate betAveen 
them. The teacher should encourage the activity of this 
faculty, and train it to a healthy and normal development. 

7. The mind should he gradually led from concrete to ab- 
stract ideas. The young mind begins with the concrete, with 
objects and their qualities. Its first ideas are perceptions of 
objects, of things that it can see and hear and feel. Its ideas 
of quality are not abstracted from, but rather associated with, 
objects. These concrete qualities it begins to conceive inde- 
pendently of the objects in which they are found, and thus it 
gradually rises to abstract ideas. From hard objects it gets 
its ideas of hardness, from kind parents and friends it obtains 
its notion of kindness, etc. This natural tendency should be 
noticed and aided, so far as possible, by the teacher. Espe- 
cially should he be careful not to lift the pupil up into 
abstractions tdo soon. He should present concrete examples 
of that which he is teaching, that the pupil may have a defi- 
nite idea of the subject to be presented before he attempts to 
consider it abstractly. He should aid the child to rise from 
things to thoughts. 

8. A child should be gradually led from pai^ticular ideas to 
general ideas. The young mind begins with the particular. 
Its first idea is of particular objects, not of general notions. 
A wan, to the young mind, is a particular person; a bird is a 
particular bird. Gradually it rises from the particular object 
to the general conception, from a percept to a concept. The 
teacher should watch this natural tendency and aid it. The 
process should not be forced, it should not be attempted too 
early ; but when the piipil is ready, it can graduall}^ be lifted 
up from the concrete into the sphere of abstract and general 



THE PRINCIPLES OF INSTRUCTION. 67 

conceptions. It should be the special aim of the teacher to 
aid the mind in rising from the particular to the general. 

9. A child should be taught to reason first inductively and 
then deductively. The child's first thoughts are the facts of 
sense. From these particular facts it gradually rises to gen- 
eral truths. By and by, after the mind has attained to some 
general principles through Induction, it begins to reverse the 
process and infer particular truths from such general princi- 
ples. It also begins to apply the self-evident truths to reach- 
ing conclusions that grow out of them. This natural activity 
of the mind should be understood by the teacher, and the work 
of instruction be done accordingly. Especial care should be 
taken not-to require deductive thought too early. In all things 
the law of nature should be implicitly followed. 

10. A child should be gradually led to attain clear concep- 
tions of the intuitive ideas and truths. Mental life begins in 
the senses ; the child's first ideas and truths are those which 
relate to the material world. But, by and by, intuition awak- 
ens into activity, and in it begin to dawn the ideas and truths 
of the Reason. The teacher should watch this natural activity, 
and be governed by it. He may aid the child in developing 
the ideas of Space, Time, Cause, the True, the Beautiful, and 
the Good, by presenting suitable occasions. He may also aid 
the pupil in reaching the self-evident truths which spring out 
of these several ideas, by particular examples and suitable 
questions. Some of the axioms of number and space are quite 
early awakened in the mind ; and the teacher can aid their 
development. 

Principles Derived from the Nature of Knowledge. 

The principles of the first class are drawn from a considera- 
tion of the nature of the mind. The principles of the second 
class are derived from the consideration of the nature of 
knowledge. The following ten principles are regarded as 
among the most important : 



68 METHODS OF TEACHING. 

1. The second object of teaching is to impart knowledge. A 
person should not only know how to obtain knowledge, but 
he should possess knowledge. He should not only know how 
to use his memory in acquiring knowledge, but he should have 
it stored with interesting and useful facts. He should not only 
know how to think, but his mind should be filled with facts 
and truths both as the materials for and the results of thought. 
Though culture, which trains to the use of the faculties, may 
be better than learning, learning is very much better than 
ignorance. The teacher should therefore aim to fill the minds 
of his pupils with the facts of history, geography, natural 
science, etc. He should hold up before them a high ideal t)f 
scholarship, and create in them an ambition for wide and 
extensive learning. 

2. Things should be taught before %oords. This principle is 
in accordance with the natural development of knowledge. 
The object existed and was known before a name was given 
to it; the word was introduced to designate the object. This 
natural order in the genesis of knowledge should be followed 
in the imparting of knowledge. The principle is also in 
accord with the natural laws of mental development. 

This principle is very frequently disregarded by the teacher. 
It is violated by requiring pupils to commit words without 
definite ideas of their meaning, and to repeat definitions with- 
out understanding them. Such a course is most pernicious 
in its influence on the mind. It leads the pupil to acquire 
wrong habits of thought, to be satisfied with the expression 
without a knowledge of the idea or fact expressed ; and deludes 
him with the idea that words, the symbols, are the realities of 
knowledge. 

3. Ideas should be taught before truths. This law is also in 
accordance with the natural law of acquisition and mental 
development. The mind has ideas before it puts them to- 
gether in judgments or thoughts. Thus it has an idea of a 
chair and the /?oo/' before it thinks the chair is on the floor. 



THE PRINCIPLES OF INSTRUCTION. 69 

So iu science, as in arithmetic and geometry, the ideas pre- 
sented in the definitions are learned before the truths which 
pertain to them. This principle is also manifest from the na- 
ture of the mind. Ideas are given by perception and concep- 
tion; thoughts are the result of judgment and reasoning; and 
the acts of perception and conception precede those of judg- 
ment and reasoning. This order should be followed in 
instruction. The etfort of the teacher should be to fill the 
mind of the pupil with ideas, both concrete and abstract, and 
subsequently to teach the truths which belong to them. 

4. Particular- ideas should be taught before general ideas. 
This principle is in accordance with the genesis of knowledge 
and the natural activity of the mind. Our first ideas are of 
particular objects, derived through the senses; following these 
come the abstract and general notions given by the under- 
standing. Thus a child has an idea of a particular bird before 
it can conceive of a bird in general, or of a class of birds ; and 
the same is true of other notions* This order, frequently 
violated in education, should be carefully followed. To depart 
from it is to invert the law of mental activity and injure the 
mind, as well as retard the acquisition of knowledge. The 
motto should be, — from the j^^it'ticular notion or fact to the 
general. 

5. Facts, or jyarticular truths, should be taught before prin- 
ciples, or general truths. A fact is a truth in the domain of 
sense ; a principle is a truth in the domain of thought. The 
former is concrete; the latter is abstract; and the concrete 
should be taught before the abstract. The former results from 
an operation of perception and judgment; the latter from an 
act of reasoning ; and an act of perception precedes an act of 
reasoning. Again, facts are particular truths; principles are 
general truths ; and the particular should precede the general. 
The principles in natural science are a generalization from 
facts ; and the mind must be familiar with the facts before it 
can generalize from them. It is thus clear that facts, or par- 



70 METHODS OF TEACHING. 

ticular truths, should be taught before principles, or general 
truths. 

6. In the physical sciences causes should be taught before 
laws. In the physical sciences we proceed from facts and 
phenomena to the laws and causes relating to them. In pre- 
senting these, the law of mental growth indicates that we 
should teach the causes of things before presenting their laws. 
The idea of cause is very early awakened in the mind. One 
of the first questions of a little child is, " Mamma, what makes 
that?" The ascertaining of the laws which control facts and 
phenomena is a later consideration. The same conclusion 
appears from the genesis of knowledge. The causes of physi- 
cal phenomena were sought for long before an inquiry was 
made for their laws. The ancients early made inquiries after 
the causes in natural philosophy and astronomy ; the attempt 
to ascertain the laws is of much more recent date. Besides, 
too, the law often flows from a correct idea of the cause, as in 
gravitation, optics, etc. It is thus clear that in teaching the 
physical sciences, the causes of facts should be considered 
before their laws. 

7. In the physical sciences^ causes and laws should be taught 
before the scientific classifications. This is indicated by tlie 
law of mental growth, and also by the genesis of the sciences. 
The mind grasps facts, causes, and laws, before it is ready for 
the grand generalizations of Natural History. These latter 
require a knowledge of particulars and a breadth of conception 
entirely beyond the grasp of the young mind. The order of 
development of these sciences also indicates the same law. 
The scientific classifications of Natural History were much 
more recent than the facts and principles of Natural Philoso- 
phy, Astronomy, etc. 

8. The elements of the Inductive Sciences should jyrecede 
the Deductive Sciences. The elements of the Inductive Sciences 
are facts and phenomena ; from these we proceed by inductive 
reasoning to laws, causes, and systems of classification. These 



THE PRINCIPLES OF INSTRUCTION. 71 

facts and phenomena are acquired by perception, and may 
thus be early presented to the learner. They come naturally 
into the mind before the ideas of the Deductive Sciences, and 
should therefore be taught before them. It is only the ele- 
ments of these sciences, however, that should precede the 
deductive sciences. The reasoning of the inductive sciences, 
by which we attain the laws, causes, etc., is more difficult 
than the first steps of reasoning in the deductive sciences ; 
and should not, except in its simplest form, be taught so 
early. 

9. Tlie formal study of the Deductive Sciences should pre- 
cede that of the Inductive Sciences. This order arises from the 
nature of knowledge in its relation to the mind. Though the 
elementary facts of the inductive sciences present themselves 
to the mind as early as the elementary ideas of the deductive 
sciences, yet the first steps of formal reasoning in the deduct- 
ive sciences are simpler than those of the inductive sciences. 
Thus, the acts of judgment in Mental Arithmetic, and the 
syllogisms of Geometr}^, are much more readily grasped by 
the young mind than the generalizations of Botany, or the 
investigations of Natural Philosophy. 

Besides, the reasoning in the mathematical sciences trains 
the mind to see the relation of premise and conclusion, and 
gives it the habit of logical activity. A mind brought up on 
facts, without the training of arithmetic and geometry, will 
be weak and illogical in its operations, and, as a rule, incom- 
petent for profound thinking. The fact that mathematics and 
logic were developed before the natural sciences also indicates 
the correctness of this principle. The fact, also, that many 
of the physical sciences, as Natural Philosophy and Astron- 
omy, cannot be developed without the aid of mathematics, 
makes the order stated in the principle a practical necessit}'' 
in respect to those branches. 

10. The Metaphysical Sciences should be the last in a course 
of instruction. The term metaphysical is here used in a 



72 METHODS OF TEACHING. 

general sense, to include Psychology, Logic, Ethics, -lEsthet- 
ics, etc. These branches are the most abstract in their 
nature, and require the most maturity of thought for their 
comprehension. They are the product of profound reflection, 
and of that ripeness of wisdom which comes with the maturity 
of age and study; and as such should not be entered upon 
until the pupil has attained considerable maturit}'' of mind 
and culture. 

Principles Derived from the Nature of Instruction. 

The first and second classes of principles are drawn from 
the first and second elements of the problem of education, — 
the nature of mind and the nature of knowledge. The third 
class is derived from the third element of this problem, — the 
nature of instruction. We give the following ten principles 
as among the most important : 

1. Primary IiiHtrucHon should proceed from the known to 
the unknoion. A pupil should begin to learn the new just 
where his knowledge of the old ends. He should be led to 
understand the new by seeing its relation to the old, and, if 
possible, its method of development from it. The known 
should be the stepping-stone to the unknown. What the 
child knows should be the light in which he is to see and 
understand that which he is to know. The elements of even 
the higher branches should be taught in this wa}'. Algebra 
should begin in arithmetic, analytical geometry in algebra and 
geometrj'-, etc. Thfs principle was first announced by Aris- 
totle, and is one of the most important in the science of 
teaching. 

2. Advanced Instruction, may sometimes proceed from the 
unknown to the known. A pupil may sometimes fix in his 
memory what he does not understand, and afterward obtain a 
clear idea of it. A definition may sometimes be committed 
to memory before its meaning is understood. An unknown 
h3'^pothesis is often assumed in an investigation, from which 



THE PRINCIPLES OF INSTRUCTION. 73 

we trace our way to known facts. A law, or method of 
operation, Avhose relation to the known is not at present 
undei'stood, may be accepted as correct, with the expectation 
that the future will make it clear to the mind. It is in this 
manner we reason in algebra by tracing our way from the 
unknown to the known; and the same method is sometimes 
used in geometr}^ We should, therefore, sometimes, in 
teaching and in study, proceed from the unknown to the 
known. 

3. Primary Instruction should be given in the concrete. 
All primary instruction should begin in the concrete. Knowl- 
edge at first must pass through the senses into the mind. 
The child must go from things to ideas and thoughts. The 
child's first lesson in numbers should be given with objects. 
The measures of denominate numbers should be presented so 
that when i^upils talk of gills, pints, etc., they may have 
definite ideas of them. The things defined in geography — 
capes, bays, isthmnses, etc. — should be learned through pic- 
tures or by some tangible representation of them. The 
elementary ideas and truths of geometry are to be taught by 
diagrams and models. From these concrete ideas the pupils 
can gradually pass to the higher abstractions of the sev- 
eral sciences. 

4. Advanced Instruction should be more abstract. The 
mind at first uses the concrete thing to aid it in rising to the 
abstract thought. At first it hobbles along, as it were, on the 
crutches of sense; but at last its wings -become plumed, and 
it can soar unaided in the higher atmosphere of abstraction. 
The concrete is then no longer needed ; the thought is grasped 
without the illustration or representative object. Concrete 
instruction should therefore not be continued too long. To de- 
pend always upon the thing for the thought will be to weaken 
the mind and lower its appreciation of the pure ideas of science. 
To teach moral philosophy with apples and potatoes is a deg- 

.radatiou of truth, as well as a source of weakness in mental 
4 



74 METHODS OF TEACHING. 

culture. The mind grows strong in its wrestling with and 
its grasp of the principles of abstract truth. 

5. Primary Instruction should he both analytic and synthetic. 
Some subjects should be presented analytically and others 
synthetically; and in many subjects, both methods should be 
combined. In teaching reading, we begin with words, then 
unite these into sentences, and afterward analyze them into 
their letters. Pronunciation also proceeds by analysis and 
synthesis ; first a synthesis of the sounds in the word, then 
the analysis of the word into its elements, and then again the 
S3^nthesis of the elements into words. Grammar should be 
taught first synthetically and then analytically^, and then the 
two methods should be united. In geography we would begin 
with the elements found in and around the school-house, pass 
out to the fields and farms, the map of the township, etc., 
which is synthetic ; and then subsequently begin at the world 
as a whole, and come down by anal3"sis to the details of the 
subject. In primar}"- arithmetic we begin with synthesis, but 
in a short time we begin to reverse the process and proceed 
also by analysis. Thus addition precedes subtraction, multi- 
jjlication comes before division, etc.; and an arithmetical solu- 
tion contains both analysis and synthesis. 

6. Advanced Instruction should be both analytic and syn- 
thetic. Some of the advanced studies should be presented 
analytically and some synthetically ; and often the two are 
united in different degrees in different parts of the same 
study. In one class of studies, analysis seems to precede and 
synthesis to follow ; in another class, this order is reversed. 
In the natural sciences, the pupil should be led to analyze for 
the elements, and afterwards to synthetize these into the 
science: facts are to be put together into classes, and phenom- 
ena to be combined so as to reach their laws and causes. In 
the mathematical sciences, the lower stage seems more syn- 
thetic, and the higher stage more analytic: the advance is 
from arithmetic to algebra, from tlie ordinary synthetic- 



THE PRINCIPLES OF IXSTRUCTION. 75 

geometiy to tlie higher aual3^tical geometry, frora plane trigo- 
nometry to analj^tical trigonometry, from synthetic mechanics 
to analytical mechanics, etc. The tendency of all the higher 
studies is towards the analytical methods of thought and in- 
vestigation. 

t. Primary ladruction should he inductive. Little chil- 
dren should be led from particulars to generals. They should 
proceed from special examples to general rules or laws which 
embrace them. In arithmetic, they should learn particular 
solutions before they learn a general rule ; and be required 
also to derive the general rules from the solution of particular 
cases. In grammar they should learn the general laws of 
speech by first seeing them presented in particular instances. 
In geography they should know the detailed facts before they 
begin to generalize them into classes and inquire after their 
laws and causes. So in learning the definitions of any branch, 
pupils should be familiar with the idea to be defined before 
they attempt to express it in a definition. Definitions when 
stat'ed in the inductive form are more appropriate to young 
pupils, than when presented in the deductive form. 

8. Advanced Instruction should he deductive. With ad- 
vanced pupils the deductive method is preferred. They 
should be taught to reason from general principles. The}'' 
should be required to grasp general laws of a subject and 
apply them to particular cases. In mathematics, the demon- 
strative method of reasoning should be employed. Thus, in 
fractions, the rules for all tlie vainous cases may be derived 
from the principles of fractions. In geography, the classifica- 
tion of the facts should be learned, and their causes and laws 
explained, as we have them treated in Physical Geography. 
The fundamental principles of grammar are to be understood, 
and to be applied in correcting and constructing language. 
In higher mathematics, we should proceed from the compre- 
hending principle to the truths contained in it. La Grange, 
in his great work on mechanics, puts the whole doctrine of 



76 METHODS OF TEACHING. 

the ph3-sical universe into an equation, and unfolds the sci- 
ence of mechanics by a discussion of this equation ; and this 
is the spirit of the modern system of mathematics. 

9. Primary Instruction should proceed from the practical 
to the theoretical. Young pupils should be drilled in doing 
rather than in thinking. In arithmetic, they should have 
abundant practice, and, at first, but little theory : they should 
be drilled in doing the work, and not in explaining it. In 
reading, the drill should be in the art of expression, rather 
than on the principles of elocution. In grammar, the primary 
object should be to teach pupils to use correct language, 
rather than to understand the principles of grammatical con- 
struction. The practice of rhetoric should precede its study 
as a science. The pupil should know how to think before he 
studies logic, the science of thought. From a correct prac- 
tice in these branches they can be led to the laws which 
govern this practice. 

10. Advanced Instruction should proceed from the theoret- 
ical to the practical. While j^ounger pupils depend on imita- 
tion for their practice, advanced pupils should be required to 
derive their practice from principles. They will thus see the 
reason for their practice, and be able to direct it independ- 
ently of the teacher or text-book. In arithmetic, they should 
be required to give a reason for the method used, and present 
a logical explanation of their work. In grammar, the princi- 
ples which govern the construction of a sentence should be 
clearly understood, and the pupil shonld endeavor to guide 
his practice by these theoretical principles. In algebra, there 
should be a discussion of the theoretical principles of the 
science, as well as a solution of problems ; and the science of 
geometry should precede tlie practice of surveying. A mind 
educated only in practice will never know anything but i)rac- 
tice ; a mind familiar with principles can originate and direct 
his practice as the circumstances maj' require. 



PART 11. 

TEACHING THE BRANCHES. 



I. OBJECT LESSOXS. 



II. TEACHING LANGUAGE. 



III. TEACHING MATHEMATICS. 



lY. TEACHING PHYSICS. 



Y. TEACHING HISTORY. 



OBJECT LESSONS. 



CHAPTER I. 

THE NATUKE OF OBJECT LESSONS. 

OBJECT LESSONS are lessons designed to give elemen- 
tary culture and instruction by means of objects. They are 
designed to afford that culture to the young mind which se- 
cures a natural development of its faculties, and also to im- 
part a knowledge of the elementary facts and principles of 
all the sciences. 

Such lessons have been introduced into nearly all our 
schools, and are regarded as an essential part of a system of 
primar}^ instruction. The credit of introducing Object Les- 
sons, as a distinct method of elementarjMnstruction, has been 
attributed to Pestalozzi ; though Locke, Commenius, and 
others advocated such instruction before him. In fact, the 
principle of Object Lessons is as old as instruction itself; for 
all good teachers have used objects in illustration of abstract 
subjects. We shall consider briefly their Value, the Prepara- 
tion required, the Method of giving an object lesson, the 
Errors to be avoided, and the Course of Instruction; and then 
present outlines and remarks to suggest a practical course to 
the young teacher. 

Value of Object Lessons. — A system of Object Lessons 
is of great value in education. Their object, as already stated, 
is two-fold ; to give both culture and instruction to the yovmg 
mind. 

(79) 



80 



METHODS OF TEACniNG. 



Object Lesso7is cultivate the Perceptive Powers. Objects are 
presented requiring pujTils to observe their form, color, quali- 
ties, etc., and thus the powers of perception ai'e exercised and 
developed. An object lesson requires a pupil to analyze an 
object carefully into its parts, to look at its details ; and this 
leads a pupil to acquire the habit of close, accurate, and ana- 
lyticid perception. 

Object Lessons give culture to the Memory. Names of ob- 
jects, their parts, qualities, etc., are to be remembered and 
recalled. This knowledge being presented in a concrete form 
makes a much deeper impression upon the memory, and is 
thus more readily fixed in the mind. Besides, the knowledge 
communicated is that which is required by the 3'oung mind, a 
knowledge of objects and facts, rather than of abstract ideas 
and truths: and is thus adapted to give normal exercise and 
culiurc to the faculty of the memor\\ 

Object Lessons give culture to the Imagination. They 
give definite pictures to the representative power as recalled 
by memory, and thus excite the imagination to create ideal 
images. The memory maybe filled with beautiful pictures of 
nature which become the type after which the imagination 
creates its ideals. A system of object lessons, thus operating 
through the memoiy, may become a source of rich culture to 
the imagination. 

Object Lesson^ give culture to the Judgment. Pupils are 
taught to compare one object with another and determine their 
relations. The colors of objects are compared with standard 
colors; the sizes of objects are determined from their relation 
to fixed standards of size ; the length and breadth of rooms, 
the height of ceilings, etc., are estimated and expressed in dif- 
ferent units; — all of which give exercise to the judgment, and 
thus strengthen and develop it. 

Object Lessonfi give culture to the Attention. The mind of 
the pupil is aroused and attracted b}'' the object and is thus 
concentrated upon it. The propensity of the mind of a child 



THE NATURE OF OBJECT LESSONS. 81 

to wander from one thing to another is thus checked, and the 
habit of mental concentration forme'd. The power of atten- 
tion is thus largely exercised and cultivated hy a system of 
object lessons. 

Object Lessons are especially adapted to give culture in the 
use of Language. They impart new words as names of 
objects, qualities, etc., which become fixed in the memory and 
enrich the piapil's vocabularj'. They also give pupils practice 
in talking, by telling what they see or have learned. They 
especially cultivate the habit of using words as expressing 
definite ideas, and thus lead to precision and accuracy in the 
use of language. 

Object Lessons train to habits of definite and accurate con- 
ception. Knowledge is most readily conveyed to the mind 
through the medium of the eye. " Seeing is believing" is an 
old adage which indicates the exactness of the knowledge 
which we gain through the sense of vision. Such definite per- 
ceptions train the mind to the habit of definite conceptions, 
of conceiving ever^^thing with exactness and completeness. A 
mind thus trained is not satisfied with the misty and shadowy 
conceptions which often pass for knowledge. 

Object Lessons are of value in im2oarting Knowledge to the 
mind. By means of object lessons, the elements of nearly 
all the ditferent sciences may be presented to children. Thus 
the elements of geometry may be taught by diagrams cut from 
pasteboard. The elements of arithmetic ma}^ be presented by 
means of objects and the numeral frame. By means of speci- 
mens of plants and insects, by charts, cards, etc., the elements 
of botany, zoology, etc., may be imparted. A system of 
object lessons, can, therefore, be so arranged as to give pupils 
a knowledge of the elementary facts of nearly all the sciences. 
Such a knowledge will prove of great value to them when, in 
after years, they are prepared to study these branches as 
sciences. 

The instruction in the elements of the physical sciences, 
4* 



82 METHODS OF TEACHING. 

as botany, i^hysiology, etc., will be of special value to the 
pupils of our public schools. AVithout such instruction, many 
of them will go out and become citizens, ignorant of the sim- 
plest facts and principles of these sciences, for thej'^ cannot be 
expected to study them from a text-book in the ordinary 
common school. With charts and suitable specimens, a fair 
knowledge of the fundamental facts of phj^siology can be given 
in a few weeks, knowledge absolutely essential to the health 
and happiness of mankind. In a similar manner, pupils 
may be made familiar with man}' of the principal facts of 
botany, natural philosoph}'^, chemistry, etc. 

Preparation for Object Lessons. — Under the Prepara- 
tion for Object Lessons we shall speak of- the Preparation of 
Material, the Preparation of the Teacher, and the Preparation 
of the Pupil. 

Preparation of Material. — Every school should be provided 
with objects suitable for giving object lessons. There should 
be a collection of specimens of leaves, flowers, minerals, bones, 
all the ordinary grains, specimens of wood, insects, coins, etc. 
Every school should be provided with a cabinet in which these 
objects are to be placed and preserved. There should also be 
charts of colors, of geometrical figures, of animals and plants, 
etc. Besides these, there should be some apparatus in the 
public schools, to illustrate the elementary facts and princi- 
ples of natural philosophy and chemistry. Every school 
should possess a glass prism, a magnet, a microscope, a 
galvanic battery, an electrical machine, etc. There are many 
little things which a teacher can make, or procure with very 
slight expense, such as a siphon, a tube for pneumatics, etc.; 
and a live teacher can raise the money among his patrons 
to })rocure man}^ of the things mentioned. 

Preparation of the Teacher. — The teacher should prepare 
himself with information upon these objects. This he can do 
by observation, conversation, and reading. By visiting shops, 
stores, mills, etc., he will be able to gain a great deal of valua- 



THE NATURE OF OBJECT LESSOXS. 83 

ble knowledge of objects and common things which he can 
use in giving object lessons. He should also consult ency- 
clopedias and other works of genei'al information. In giving 
lessons on the elements of the different sciences, as geometry, 
physiology, botany, etc., he can select the facts he needs from 
the text-books on these subjects. 

The teacher should also prepare himself upon the method, 
as well as upon the matter of an object lesson. He should 
systematize his knowledge, and arrange it in the order in 
which it is to be presented. An outline should be prepared; 
and, if there is time, committed to memory, so that the lesson 
may not be loose and rambling, but have a system, and be di- 
rected toward a definite end. 

Preparation of the Pupil. — The pupil should also be re- 
quired to prepare for the lesson. He should first be required 
to observe all he can of an object, that he may have an oppor- 
tunity for the culture of his perceptive powei's. He may tlien 
make inquiries of older persons, and gain what information 
he can from them. Lastl^y, he may go to books treating of 
the subject, and learn the recorded observations of others. 
This last method is usuall}^ the easiest ; and care should be 
taken that the pupil does not resort to it first, and thus, 
though he" may obtain knowledge, lose the primar}^ object of 
tjie lesson, — the culture of his senses. 

The Method. — In giving an object lesson, the pupils should 
first be allowed to tell all they know about the object. This 
will encourage them to prepare for the lesson, and add interest 
to it, as children love to tell what they know. Secondly, the 
teacher should lead the pupils to find out all they can of what 
the}^ have not j'et observed respecting the object. Knowl- 
edge thus gained will be more interesting to them than if 
tliey are told the things by the teacher ; and will also stimu- 
late the power of investigating for themselves. Lastly, the 
teacher should communicate such knowledge as is adapted to 
the pupil and is appropriate to the subject. 



84 METHODS OF TEACHING. 

TcUinrj iJieir Knowledge. — The puijils should first be allowed 
to tell what they know. This will give interest to the study, 
for children love to talk as the birds love to sing. It also 
cultivates the habit of speaking from the actual presence of 
ideas in the mind; and of talking to express thought, and not 
to repeat words. This is of supreme value in every lesson. 
In this breaking away from the repeating of words, and the 
expressing of some real idea in the mind, is found the great 
reform in modern school education. 

Finding Out. — The second step in an object lesson is to 
lead the pupil to find out knowledge for himself. Here the 
teacher begins the work of instruction; and this is the key- 
uote of all good teaching. We should smooth and brighten 
the pathway of the child all we can ; but we must also help 
children to help themselves. We must make them seekers 
after truth ; and not mere receivers of truth. To teach a 
child to long for truth is better than to give it truth; to 
excite an appetite to know is far better than to satisly this 
appetite. We may thus make him an original truth-seeker, 
lay the foundations of intellectual power, and develop the 
spirit which gives us the world's philosophers. 

Communicate Knowledge. — The last step is that of commu- 
nicating knowdedge. In the previous step the teacher was a 
guide to knowledge ; here he becomes the source of knowl* 
edge. All instruction should have a teacher at its heart ; it 
must contain the central element of personality. This is 
the crowning element of the teacher's work ; the influence of 
his own thought and feeling in instruction. A large-souled 
man or woman projects his personality in his instruction and 
irradiates what he communicates. He puts a charm in knowl- 
edge not otherwise seen, and inspires the hearts of his pupils 
with a love for learning not otherwise felt. Only the man or 
woman who can do this is a teacher in the high sense of the 
word, and it needs the best and rarest traits of character to 
attain it. 



LESSONS ON FORM. 85 

Errors to he Avoided. — The teacher should be careful not 
to mistake the nature and design of an object lesson. He 
should remember that the primary object is to awaken the 
faculties of the 3"0ung mind into a natural and healthful ac- 
tivity ; and that the secondary object is to present a knowl- 
edge of the elementary facts of the different sciences. He 
should be careful, therefore, to adapt his instruction to the 
accomplishment of both these objects. 

The teacher should be especially careful not to teach words 
without ideas. The thing to be named should first be clearly 
presented to the mind ; and then the name be given as a 
necessity to express the idea of it. Thus every new word 
becomes an expression of a definite and clearly defined con- 
ception. Young teachers should be especially careful to 
guard against the liabilit}^ to teach names without correspond- 
ing ideas. 

Teachers should be careful also not to give matter that is 
beyond the capacity and appreciation of the pupil. Having 
no text-book to guide them in these lessons, thej- must rely 
on their own judgment ; and, without experience, they will find 
that it is an easy matter to get beyond the understanding and 
appreciation of the pupil. Great care must be taken to avoid 
this error,' which is a very common one. 

Course of TnstrncUon. — A Course of Object Lessons 
should embrace Lessons on Form, Color, Parts of Objects, 
Qualities of Objects, Facts concerning Objects, and the Ele- 
ments of several of the sciences, as Botany, Physiology, etc. 

I. Lessons on Form. 

The Lessons on Form should include all the ordinary geo- 
metrical figures. These lessons may be given with figures 
made of wood or pasteboard, with diagrams on the board, with 
geometrical charts, etc. There are sets of geometrical figures 
prepared which should be in every school-room. The pupils 



86 



METHODS OF TEACHING. 



ahoiild be required to draw these figures on tlie slate and 
blaclvboard. This will afford pleasant emplo^-ment for them 
and keep them out of mischief, as well as give them instruction. 
We present a brief outline of the lessons on geometrical 
forms for the aid of young teachers. 



Elements 



Polygons 



('Lines. 
' Angles. 

Surfaces. 

Volumes. 

( Triangles. 
I Quadri laterals. 
! Pentagons. 
I Hexagons. 
I Heptagons. 
l_ Octagons. 



( Straight. 

I Curved. 

Lines ■{ Broken. 

Parallel. 

[oblique. 



Triano-les 



('Square. 
C Parallelograms <| rSiS.' 



Quadrilaterals <J 



1 Rhomboid. 



Trapezoid. 
[Trapezium. 



( Prism 



f Cube. 



Parallelopipedon. 
„ , , , , Triano-ular Prism, etc. 

Polyedrons ^ p.-ramid. 

I. Frustum of Pyramid. 

C Cylinder. 

Round Bodies <j p^Ttum of Cone. 
[ Sphere. 



C Acute. 
Angles^ Obtuse. 
Uiglit. 

/ ^ C Equilateral. 
I ~ < Isosceles- 
I ■/} ( Scalene. 

I £ C Acute-angled. 
I M < Obtuse-angled. 
L .^ ( Kight-augied. 

( Circumference. 

Diameter. 

Radius. 

Arc. 

Chord. 

Segment. 

Sector. 

Tangent. 

Secant. 

Quadrant. 

Semi-circle. 
, Semi-circumference. 



C Parabola. 
Conic Sections < Ellipse. 

( Hyperbola. 

C Cycloid. 
Other Bodies < Catenary. 
( Spirals, 



Circle 



To the older pupils some of the truths of geometry may be 
presented, like those found under Elementary Geometry. This 
will be the only opportunity the large majority of pupils will 
have to become familiar with these truths, which will be found 
of real practical value in life. 

II. Lessons on Color. 

The pu]-»il should receive Lessons on Color. He should be 
taught to distinguish and name all the principal colors. Such 
lessons can be given only by visible illustrations, since color 



LESSONS OX COLOR, 87 

can be learned only by seeing it. Ever}'' school should, there- 
fore, be supplied with a "Chart of Colors," and a "Box of 
Small Color-oards." It will be well, also, to have specimens 
of worsteds, pieces of silk, colored papers, flowers in their 
season, autumn leaves, etc. There should also be a glass 
prism to analj^ze a sunbeam, and colored crayons for the 
blackboai'd. 

The teacher will first present the principal colors on the 
color chart, and then pass around the small cards or hold 
them up before the pupils, and have them name the colors. 
Worsteds, flowers, leaves, and other colored objects, may be 
used in the same way. 

The teacher may also explain the nature of color, that it is 
a modification of light, and that all colors exist between the 
extremes of light and darkness. He may also explain the 
nature of light, that it is the vibration of a very rare fluid 
called ether^ pi'oducing its effects on the e^^e somewhat as the 
vibration of air produces the sensation of sound on the ear. 

It will be well, also, to call the attention of the pupil to the 
phenomenon of color-blindness. Man^^ persons can scarcely 
discriminate between shades of the same color; others cannot 
distinguish between colors which are strikingly opposed to 
one another. There are persons who can only distinguish 
black and white, and others who cannot tell red cherries from 
green leaves, except by their shape. Amusing incidents are 
related in illustration of this peculiarity. An English naval 
officer chose a blue coat and red trousers, supposing them to 
be of the same color; and a tailor mended a black silk vest 
with a patch of crimson. Bartholomew, the sculptor, could 
not distinguish green from red, and painted the cheeks of a 
lady's portrait green. Accidents have occurred on railroads 
on account of the engineer or flagman mistaking colors, and 
candidates for these positions are now examined as to their 
powers in this respect. 

Calkins, who gives the above facts, also tells us that out of 



ba METHODS OF TEACHIXG. 

forty bo3^s in a school in Berlin, five could not distinguish 
between common colors. " From calculations based on exami- 
nations made in England and Scotland, it appeared that one 
person out of every fifteen was unable to distinguish all the 
ordinary colors ; one in fifty-five confounded red with green ; 
one in sixty, brown with green ; one in fort3'-six, blue with 
green." . 

It is not necessary to represent the colors in this work, as 
there should be a chart of colors in ever}^ public school. 
Each teacher should have a copy of Calkins's New Primary 
Object Lessons, published b}^ the Harpers, New York. The 
following facts and definitions will suggest to the teacher a 
proper course of instruction in color. 

There are three Primary colors, — Red, Yellow, anti Blue. These are 
called primary colors, because all other colors may be formed from them. 

The three primary colors, if mixed together, will produce white light. 
Paint them on a wheel in three equal parts, then revolve the wheel, and 
it will appear white. 

There are seven Prismatic colors, — Yiolet, Indigo, Blue, Green, Yel- 
low, Orange, and Red. These are called i)rismutic colors because a ray 
of white light, passing through a glass prism, will be divided into these 
seven coloi's. The order of these colors can easily be retained by the 
word vibrjyor. 

Secondary colors are those which are formed by mixing the primary 
colors. The secondary colors are, Orange, Green, Indigo, and Violet, 
or, instead of the last two. Purple. 

Orange is formed by mixing red and yellow. Green is formed by 
mixing blue and yellow. Purple is formed by mixing red and blue. 

The different varieties of Red are Maroon, Crimson, Scarlet, Carmine, Ver- 
milion, and Pink. Tlie different varieties of Yelloio are Citron, Lomon, 
Canary, Straw, and Yellow. The different varieties of JJlue are Indigo, 
Ultramarine, Prussian Blue, Light Blue, and Sky Blue. Tlie different varie- 
ties of Green are Olive Green, Emerald, Pea Green, and Bright Green. Tlie 
different varieties of Purple are Royal Purple, Purple, Violet, Lilac, and Lav- 
ender. The different Varieties of Oraw/e are Dark Amber, Orange, Salmon, 
Buff, and Cream. 

Brown is usually composed of red, yellow, and black, sometimes modified 
by the addition of white. The different varieties of Brown are Chocolate, 
Russet, Snuff, Drab, and Tan. Gray is composed of black and white, with a 



OBJECTS AND THEIR PARTS. 89 

sli^lit mixture of red, yellow, or black. The different varieties are, Slate, 
Pearl Gray, Steel Color, and French Gray. 

Tcrtuiry colors are formed by mixing two secondary colors, or three 
primary colors in the proportion of two parts of one and one part of each 
of the other two coloi's. The tertiary colors are Citrine, Olive, and 
Russet. 

Tliere are several varieties of colors, indicated by the terms Shade, Tint, Hue, 
and Tinge. A Shade is formed by mixing black with any color, so as to make 
it darker than the original color. A Tiyit is formed by mixing wldte with any 
color, so as to render it lighter than the original color. A Hue is formed by 
combining two colors in unequal proportions ; as, a little yellow mixed with 
pure red gives scarlet, a hue of red. A Tbuje is a slight coloring or tincture 
added to the principal color; thus, green, if it has a slight coloring of yellow, 
is said to have a tiufje of yellow. 

Two colors wliich, when united, produce white light, are said to be 
Complementary. Tlius, red and green, orange and blue, yellow and 
purple, are complementary colors. 

By the Harmony of Colors, we mean that relation of certain colors, 
which gives special pleasure to tlie eye. The complementary colors are 
harmonious. Since two colors are harmonious, which when mixed 
together produce white light, for harmony of color we must have one 
prlmarj^ and one secondary color. The teacher may show the pujiil 
that in the scale of prismatic colors, the harmonious colors stand to each 
other in the relation of fourths, like one of the richest cliords in music. 

The teacher may show the application of the harmony of colors, by 
asking questions about ladies' wearing apparel, furnishing a room, 
arranging a bouquet, etc. 

III. Objects and Their Parts. 

Pupils should have lessons on Objects and their Farts. 
They should be taught to know and name the parts of objects. 
For this purpose, teachers should have a suitable collection 
of objects in the school-room. The information concerning 
these objects, the teacher'can obtain in various waj'^s, as here- 
tofore explained. The following outlines, selected from Shel- 
don's Object Lessons, will suggest a course to the young 
teacher : 



90 



METHODS OF TEACHING. 





a. Shaft. 










(I. Mouth 




^ 




1. 


Wood 


ti 


2. Ring. 

3. Barrel. 




^ 


ri- 


Bo^M3:B£k. 






2. 

3 


Lead. 
Head. 


4. Lip. 




C/2 


<! 

1 
12. 


U. Canal. 




S- 


4. 


Point. 


^ 


5. Wards. 
^6. Grooves. 




C<! 


ri. Whorls. 
Spire < 2. Sutures. 
[3. Apex. 


03 


5 
6 

L 


Number 
Maker's Name, 
or Trade Mark. 




'1. Blade. 








'1. Surface. 








f 1. Bowl. 




2. Bows. 








2. Faces. 








2. Handle. 


u 


3. Limbs. 








^ 3. Edges. 






& 


3. Upper Rim. 


O 


4. Rivets. 








g J 4. Milling. 






3 


] 4. Lower Rim. 


1" 


.5. Edges. 








1 .5. Impression. 







1 .5. Bottom. 


t» 


6. Back. 








id 6. Image. 






«' 


6. Inside. 


T)^ 


7. Point. 








7. Superscription. 




7. Outside. 




^8. Shaft. 








8. Date. 








8. Edges. 


e 


'1. Head. 










f 1. Stem 






1. Nut. 

2. Catch. 


C" 


2. Point. 










2. Peel. 






t^ 1 


,3. Shaft. 










3. Pulp. 






1. Handle { 3. Shaft. 




1. Posts 1 2" 
r 


Front. 
B.^ck. 


q5 

a 

< 


4. Juice. 
.5. Veins. 
fi. Dimples. 






4. Ferule. 
.5. Number, 
f 1. Border. 




1 


Front 




7. Eye. 




d 


2. Cup ^ 2. Rim. 




2. Rounds < 


2 


Side. 




8. Core. 








{■6. Edge. 


^ 


3. Back. 


3! 


Back. 




9. Seeds. 
10. Seed-case. 




,3.To„,uejJ;^~Pp,^. 




4. Seat. 
















.5. Pillars. 








r 1. Bail. 






f 1. Shell. 


d 


6. Spindles. 








2. Handle. 






1 2 Kernel. 


1-1 


7. Slats. 








3. Ears. 




a fl. 


Nut -i 3. Point. 




8. Balls. 






^ 


4. Body. 







4. Scar. 




9. Beads. 






■3 


.5. Staves. 






< ' 


5. Membrane. 




10. Scallops. 








6. Hoops. 




( 1. Scales. 




11. Brace. 






^ 


7. Bottom. 

8. Rivets. 




^ [s- 


Cup I 2. Edges, 
i 3. Stem. 




1. Upper. 

2. Sole. 








9. Chime. 
10. Crole. 








1. Rivets. 




8. Heel. 
















2. Frame. 




4. Tip. 
















3. Heel. 




5. Eyelets. 

6. Binding. 












' 1. Handle ■! 

1 


4. Sides. 

5. Back. 


aj 


7. Seams. 
















6. Spring. 


o 

J3 


8. Tongue. 










. 






7. Grooves. 


CO " 


9. Lining. 










•a 






8. Plate. 


2 


10. Insole. 












2. Joint - 


Pivot. 




11. Counter 
















12. Shank. 










r-l 




fl. Edge. 




13. Welt. 














1 2 Point. 




14. Strings. 

15. Buttons. 












.3. Blade 


1 3. Back. 
1 4. Notch. 




.16. Vamps. 














.5. Sides. 
























_ 


). Maker's name 



QUALITIES OF OBJECTS. 



91 



Every teacher of a primary or public school should go to 
work and collect facts coucernirig other objects, and prepare 
outlines for giving lessons upon them. No teacher should be 
without a copy of Sheldon's Object Lessons^ published by 
Scribner, Armstrong & Co. 

lY. Qualities of Objects. 

Pupils should be taught to distinguish and name the Quali- 
ties of Objects. These qualities should be taught, not ab- 
stractly, but in connection with the objects in which they are 
found. The pupil should be led to perceive the quality in 
the object, and thus obtain a clear idea of it, and then its name 
may be presented and fixed in the memory. 

The following list of qualities will suggest to the teacher 
his work in this respect : 



Hard, 


Brittle, 


Bound, 


Woven, 


Soft, 


Flexible, 


Square, 


CeUular, 


Rough, 


Pliable, 


Angular, 


Tubular, 


Smooth, 


Elastic, 


Triangular, 


Netted, 


Stiff, 


Ductile, 


Rectangular, 


Fibrous, 


Limber, 


Malleable, 


Cylindrical, 


Porous, 


Light, 


Buoyant, 


Spherical, 


Twisted, 


Heavy, 


Sonorous, 


^ Concave, 


Indented, 


Solid, 


Fusible, 


Convex, 


Crystallized, 


Liquid, 


Volatile, 


Spiral, 


Membranous, 


Transparer 


It, 


Natural, 


Saline, 


Translucent, 


Artificial, 


Odorous, 


Opaque, 




Durable, 


Aromatic, 


Brilliant, 




Compressible, 


Edible, 


Adhesive, 




Pulverable, 


Tasteless, 


Tenacious, 




Soluble, 


Pungent, 


Amorphous, 


Insoluble, 


Emollient, 


Inflammable, 


Impervious, 


Sapid, 


Combustible, 


Serrated, 


Nutritious. 



V. Elements of Botany. 

Object lessons on the Elements of Botany may embrace the 
floivei- and its parts, the leaf and its parts, the names of 
leaves from their /or?ns, the names of leaves from their maj-- 
gins, the names of plants, trees, etc. 



92 



METHODS OF TEACHING. 



The following outline will suggest to the teacher a short 

course in botany: 

f Calyx i Sepals. 
I Corolla -{ Petals. 

(Filament. 
Anther. 
Pollen. 
Flower ( Style. 

Pistils < Stigma. 
( Ovary. 
[ Peduncle. 



Parts 

of 
Leaf 



Margins 

of 
Leaves 



f Entire. 
Serrate. 
Dentate. 
Crenate. 
Repand. 
Lobed. 



Bases 

of 
Leaves 



Apices 

of 
Leaves 



f Blade. 
Midrib. 
Vein. 
Veinlets. 
Paracliym. 
Margin. 
Apex. 
Base. 
Petiole. 
Stipule. 

' Acute. 

Acuminate. 

Obtuse. 

Truncate. 
- Retuse. 

Obcordate. 

Emarginate. 

Mucronate. 
1^ Cuspidate. 



Shape 

of 
Leaves 



f Cordate. 

Reniforra. 

Auriculate. 

Hastate. 

Sagittate. 

Oblique. 

Tapering. 

Clasping. 

Connate. 
. Decurrent. 
' Orbicular. 
Rotundate. 
Elliptical. 
Obltmg. 
Linear. 
Acicular. 
Deltoid. 
Ovate. 
Lanceolate. 
Cordiform. 
Hastate. 
Sagittate. 
Peltate. 
Runcinate. 
Pedate. 
. Lyrate. 

In every public school there should be charts containing 
diagrams of all these forms, and the teacher should obtain 
specimens of them from nature. A work recommended for 
the teacher is Miss Youmans's Fii^st Book in Botany, published 
by Appleton & Co. 

There should also be a course of instruction on insects, birds, 
and other animals, which may be given by colored engravings, 
specimens, etc. 



f Petal I Limb, 
i Claw. 
Cruciferous. 
Rosaceous. 
Liliaceous. 

f Banner. 
Corolla I Papilionaceous < Wings. 
I Keel. 
Rotate. 
Campanulate. 
Salver-form. 
Funnel-form. 
. Labiate. 



LANGUAGE. 



CHAPTER I. 



THE NATURE OF LANGUAGE. 



LANGUAGE is the insti'ument of thought and the medium 
of expression. The term is derived from lingua^ the 
tongue, and meant primarily that whicli came from or was 
moulded by the tongue. 

The primar3^ idea of language is that it is the means of 
expressing our ideas and thoughts. It is the means by which 
we convey ideas and thoughts from one mind to another. It 
is seen, moreover, that language is necessary to thought ; that 
we think by means of language. Sir William Hamilton and 
other philosophers hold that there can be no thinking without 
thought symbols ; that is, without words. If we add this 
further use of language to the primary idea of expressing 
thought, we have the definition given above. 

Language, as it now exists, means also the embodiment of 
thought in words. It is thought expressed, as well as the 
power of expressing thought ; it is thought made tangible to 
the senses of sight and hearing. Human language has been 
figuratively called the outward type or form which thoughts 
and the laws which regulate them, impress on the material of 
sound. Plato saj-s, "reason and discourse are one," the 
former being the conA'ersation of the soul with herself, with- 
out the intervention of sound ; the latter being this conversa- 
tion made audible by sound. Max Miiller says, — "Language 
and thought are inseparable. Words without thoughts are 

COG) 



94 METHODS OF TEACIIIXQ 

dead sounds ; thouohts withont words ai'e nothing. To think 
is to speak low ; to speak is to think aloud. The word is the 
thought incarnate." Language is of two kinds ; Oral and 
Written. 

T. Spoken Language. 

Definition. — Oral Language consists of a combination of 
articulate sounds to express ideas. An articulate sound is 
literally a jointed sound, and is thus distinguished from a 
continuous sound, as a cry, etc. The sounds which are united 
in the formation of spoken words are called elementary 
soitnds, and consist, in our language, of about forty. The ex- 
act number has not been definitely determined by orthoepists. 

Orif/in of Laufjaage. — There are two general theories for 
the origin of spoken language, — the theory of Divine Origin, 
and the theor}^ of Human Origin. The theory of a divine 
origin assumes that God gave man a language when he 
created him, by which he could immediately communicate his 
ideas and thoughts. In favor of this theory, it is argued that 
God pronounced His work to be perfect, and that man would 
not have been perfect without the gift of a language. It is 
also claimed that man must have had a language, or he could 
not have conversed with God, as he is represented doing in 
the Garden of Eden. 

The theory of a human origin assumes that man had origin- 
ally no language, but merely the power to form a language. 
He had the gift of speech as he had the gift of reason, and he 
formed his own language as he has formed the other arts and 
sciences. In favor of this theory, it is claimed that it is 
natural to suppose an analogy between the development of 
language and the development of the arts and sciences. Man 
was not created with a knowledge of the science of geometry, 
but with powers by which he could originate it. Language- 
was an evolution from man's capabilities, the same as the 
sciences. 



NATURE OF LANGUAGE. 95 

It is also claimed that the history of languages shows a 
growth and development from rude beginnings to a more fin- 
ished form. It is further held that the Bible presents this 
view, for it says that the animals were brought before Adam 
to see what he would call them, " and whatever Adam called 
them, that was the name thereof." It is further held that so 
strong is this power of speech that children at the present 
lime, if placed where they never heard a word spoken, would 
form a language- of their own. Instances are recorded in 
which the children in a family have actually formed a language 
for themselves. It is now the general belief of writers upon 
the subject that language is of human, rather than of divine 
origin. 

Theories of Ovighi. — Assuming that language is of human 
origin, the question arises, — How or in what way was it 
formed ? Several theories have been offered as the answer to 
this question, which have been distinguished as the theories 
of Imitation^ Interjections, and Verbal Boots. The first and 
second are also called the Mimetic and Exclamatory theories, 
and the last the theory of Phonetic Types. 

Theory of Imitation. — The theory of Imitation assumes 
that words originated in the imitation of the sounds of nature. 
Thus man heard a dog say how-wow, and he called it a how-wow. 
He heard a sheep say haa, and he called it a haa. He heard 
a bee buzz, and he imitated the sound, and buzz became the 
name of a bee. It was supposed that by this principle of 
onomatopoeia originated many such words as crash, hiss, 
roar, crack, thunder, etc. 

This theory, which was once popular, is now generally dis- 
carded by philologists. It is probable that very few words 
originated in this way. Many words which were supposed to 
have thus originated, have been traced to quite a diffeix'nt 
origin. Thus, squirrel, "v^^hich was supposed to be an imita- 
tion of the noise made hy the animal, has been found to mean 
a " shade tail ;" cat, or the German katze, which was supposed 



96 METHODS OF TEACHIXG. 

to represent the noise made by the eat, comes from an expres- 
sion meaning "an animal that cleans herself;" thunder^ which 
was supposed, to represent the rolling noise of the clap, comes 
from tan^ signifying to atretcli. A few words, as whipjjoor- 
ivill, cuckoo, etc., had their origin in this wa^' ; but such words 
are sterile, have no reproducing power, and thus are not con- 
sidered to be true words. 

Theory of Interjections. — The theor}- of Interjections as- 
sumes that all words originated from primary utterances of 
emotions. Thus all races emit certain similar ejaculations to 
express similar feelings of pain or joy. The cry, the groan^ 
the laugh, etc., are common to all mankind. These natural 
utterances are supposed to have been the basis of language. 
There is no authority, however, for the theory, and it has now 
no supporters. Max Muller calls this the Pooh-pooh theor3^ 
He also calls the theory of Imitation the Bow-wow theory. 

Theory of Verbal Boots The theory of Verbal Roots 

assumes that man was primaril}' endowed with a '• linguistic 
instinct" by which he gave origin to verbal utterances. These 
primary utterances were \ery numerous ; many of them per- 
ished in the struggle for life, but those which remained 
became the parents of all the other words of the language. 
These expressions were verbal in their character, and hence 
ai-e called the verbal roots of the language ; and the theory- is 
known as the theory of Verbal Roots. 

In favor of this theory, it may be argued that a large part 
of the language can be traced back to verbs. If we open the 
dictionary for the etymology of a word, we usuall}' find that 
it is derived from a verb. The preposition except was origi- 
nall}^ the past participle of the verb to except, etc.; and even 
the conjunction if had its origin in a verb gif, to give or 
grant. The importance of the verb, which means the word 
(verbnm), is also a consideration in favor of the theor}-. The 
Chinese call verbs lioing words, and all others, dead words. 

The theory, however, is not generally accepted. Whitney 



NATURE OF LANGUAGE. 97 

ridicules it, calling it the Ding-dong theovy^an epithet derived 
from Miiller's illustration, that everything struck rings, and 
that the mind of the primitive man, when struck by the objects 
of nature, rang out with a sound. The theory was first pro- 
posed by Heyse, and advocated by Miiller, who, however, now 
discards it. 

The True Theory. — The true theor}^ for the origin of lan- 
guage is, that it is a natural outgrowth of man's mental and 
vocal powers. Man was gifted with the power of thought and 
feeling, and the faculty of expression. He Avas moved by his 
desires and impulses to embody his thought in vocal utter- 
ances. These utterances were made partly by chance, aided 
perhaps . by the imitation of the sounds of nature. The}^ 
gradually developed into more and more perfect forms, 
through the necessity and pleasure of communication, and the 
progress of the race in refinement and intellectual culture. 

In this evolution, thought and language, on account of their 
intimate relation, must have gone hand in hand. Which pre- 
ceded the other, has been a question among philosophers. 
G-eiger holds that man was guided in his utterances by that 
which he saw, and that the use of language, in a measure, pre- 
ceded and produced reasoning. Prof. Whitney and others 
maintain that thought is anterior to language, and independ- 
ent of it ; and that thought need not be internally or externally 
expressed to be thought. In fact, however, the two must have 
developed together, and language not onl}- expressed thought 
but aided it in its origin and growth. 

TJt-e Primitive Lnngudge. — Which was the primitive lan- 
guage is not positively known; the question, however, is a 
very old one. Herodotus tells us that Psammitichus, King 
of Egypt, to ascertain the most ancient nation, gave two new- 
born children to a shepherd to be brought up so as never to* 
hear any words spoken. When they were about two years 
old, they held out their liands for bread and cried " Becos," 
whieli they contiuued to use for the same purpose. Tiiis being 



98 METHODS OF TEACHING. 

reported to the kiug, he inquired what people called bread 
'■ Becos" ; and discovered that it was the Phrygians, and thus 
inferred that the Phrygian was the primitive language.' James 
IV. of Scotland, in order to ascertain the primitive language, 
placed a deaf and dumb woman with two infant children, on the 
solitary island of Inchkeith, to see what language they would 
use when they came to the age of speech. A Scotch histo- 
rian, who gives the account, naively remarks, "Some say they 
spoke good Hebrew ; for my part, I know not, but from report." 

Tlie JEiifflish Lauf/uage The historical origin and devel- 
opment of the English language is well known. The island 
of Britain was originally settled by the Celts, a branch of the 
great Indo-European race, which had moved west, on the wave 
of emigration, from Central Asia. Remains of the same race 
are found all along the Atlantic coasts of Europe, though they 
were mainly congregated in Spain, Gaul, Britain, and the 
adjacent islands. 

In the year 55 B. C, the Romans under Julius Ceesar, 
who had previously conquered Gaul, passed over into Britain 
and subdued and held possession of it for nearly five centu- 
ries. Yer^' few Latin words, however, were introduced into 
the language of Britain during the Roman occupation, per- 
haps not more than a dozen. A few names of places derived 
from cast)'a, a, camp, remain; as Chester, Westchester, Chi- 
chester, Winchester, Lancaster, which indicate that the mili- 
tary camps of the Romans became centi*es of trade, and grew 
into towns. 

About the fifth century the northern barbarians invaded 
Southern Europe, and threatened the overthrow of the corrupt 
and imbecile Roman provinces. Rome, to defend herself, was 
obliged to withdraw her forces, and leave Britain to contend 
• with the tribes that surrounded her. In the year 451 the 
Saxons, a Teutonic tribe from the southern shores of the Bal- 
tic, under the lead of the two brothers, Hengist and Horsa, 
came over and settled on the shores of Kent. Swarms of the 



NATURE OF LANGUAGE. 99 

same tribes followed from time to time, and drove the Celts 
into the mountains of Wales and Cornwall. In the year 827, 
about four centuries after the invasion, seven independent 
kingdoms had been established, known as the Saxon Hep- 
tarchy. The most important of these Teutonic tribes were 
the Jutes, the Angles, and the Saxons. The Angles, who 
seem to have been distinguished for their energy and intelli- 
gence, though small in numbers, gave their name to the island, 
England being a modification of Angle-land. The Saxon lan- 
guage thus became the language of the island, a few Celtic 
names being mixed with it. During the ninth and tenth cen- 
tui'ies, the Danes, a Scandinavian tribe, made incui'sions 
and conquests, and introduced a few words into the Saxon 
language. 

In 10G6, William, Duke of Normandy, invaded England, 
and, by the decisive battle of Hastings, established himself 
on the English throne. He divided the island among his fol- 
lowers, and determined to incorporate the Saxons with the 
Normans, and introduce the Norman language as the language 
of the island. To effect this, he ordered that the j^outh in the 
schools should be instructed in the Norman language, that 
the pupils of the grammar schools should translate Latin into 
French, and that all conversation in them should be carried on 
in one of these languages. Pleadings in the courts were to 
be in French, deeds were to be drawn in this language, no 
other tongue was used at court and in fashionable society. 
So great was this influence, that English nobles themselves 
affected to excel in the foreign dialect. The mass of the peo- 
ple, however, at first resisted this change ; but finally, as the 
two peoples intermingled, their languages intermingled also, 
and the English language is the result, — the basis of it being 
Saxon, and about one-third of it being from the Norman 
French. 

The Norman French was mainl}- a Latin tongue. The Nor- 
mans, or Northmen, were originally the inhabitants of ancient 



100 METHODS OF TEACHING. 

Scandinavia — Norwaj^, Sweden, and Denmark. • Under Rollo, 
about 912 A. D., they had conquered and settled in a province 
of France, where in time they adopted the religion and lan- 
guage of the French. The French was a corrupt form of 
Latin, formed by the mixture of the Latin introduced into 
Gaul by the Romans, and the language of the Germanic tribes 
who afterwards conquered it. The Norman conquest thus 
introduced a large element of Latin into the English lan- 
guage. A large number of Latin words wei'e subsequentl}' 
introduced by Latin scholars ; and in the same way the Greek 
element of our language originated. Words of other lan- 
guages have been introduced by business, commercial rela- 
tions, etc. The English language is thus a composite tongue, 
its basis being the Anglo-Saxon, with about one-third Latin, 
a sprinkling of Greek, and a few words from other tongues. 

Classification of Lanf/imge. — Attempts have been made 
to classify the diffex*ent languages, but no scheme has been 
given which is universally adopted. Max Miiller speaks of 
four distinct stages in the growth of language : the first being 
the epoch of roots; the second being the epoch of juxtaposi- 
tion and concentration, as in the Chinese ; the third being the 
agglutinative stage, represented by the Turanian tongues ; 
and the fourth being the inflexional stage, or stage of amal- 
gamation, represented by the Semitic and Ar3^an languages. 

An arrangement based on outward differences of form, that 
will give quite a clear idea of the subject, divides languages 
into three classes ; the Monosyllabic, the Agglutinated, and 
the Inflected. The Monosyllabic class contains those lan- 
guages which consist only of separate unvaried monosyllables. 
The words do not naturally afliliate, and the scientific forms 
or principles of grammar are either wanting or very imperfect. 
It includes the Chinese and Japanese languages and also the 
dialects of the North American Indians. In the Agglutinated 
languages, the words combine only in a mechanical way ; 
they have no elective afiinity and manifest no capabilities of a 



NATURE OF LANGUAGE. 101 

living organism. Prepositions are joined to nouns and pro- 
nouns to verbs, but not so as to make a new form of the 
original word, as in the inflected tongues. This class is called 
Turanian, from Turan, a name of Central Asia. The principal 
varieties of this family are the Tartar, Finnish, Lappish, Hun- 
garian, and Caucasian. 

The Inflected languages have a complete interior organiza- 
tion, with mutual relations and adaptations. They differ from 
the Monosyllabic as organic from inorganic forms ; and from 
the Agglutinated as vegetable growths from mineral accre- 
tions. This class includes the culture of the world, and in 
their history lies embosomed the history of civilization. 

To this class belong two great families, the Semitic and the 
Indo-European. The Semitic embraces the languages native 
to Southwestern Asia, supposed to have been spoken by the 
descendants of Shem. It includes the Hebrew, Aramaean, 
Arabic, the Ancient Egyptian or Coptic, the Chaldean, and 
Phoenician. The Semitic languages differ widely from the 
Indo-European in their grammar, vocabulary, and idioms. 
On account of the pictorial element in them, they may be 
called the metaphorical languages, while the Indo-European 
may be called the philosophical languages. 

The two principal languages of the Indo-European stock 
are the Aryan and the Grajco-Italic, or Pelasgic. The word 
Aryan (Sanskrit, Arya) signifies ^veil-born, and was applied 
by the ancient Hindoos to themselves in contra-distinction 
from the rest of the world, whom they considered base-born 
and contemptible. The Pelasgic comprises the Greek family 
and its dialects and the Italic family, the chief subdivisions 
of which are the Etruscan, the Latin, and the modern lan- 
guages derived from the Latin. The other Indo-European 
families are the Lettic, Slavic, Gothic, and Celtic, with tlinir 
various subdivisions. 

The Indo-European languages are noted for their variety, 
flexibility, beauty, and strength. They are remarkable for 



102 METHODS OF TEACHING. 

vitality, and possess the power of regenerating themselves 
and bringing forth new linguistic creations. They render 
most faithfully the various workings of the humaii mind — its 
wants, its aspirations, its passions, its imaginings — and em- 
body and express the highest products of its thought and 
philosophy. Through them, modern civilization, by a chain 
reaching through many thousand j-ears, ascends to its primi- 
tive source. 

II. Written Language. 

Written Language is the art of expressing ideas and 
thoughts by means of visible symbols. It is the embodiment 
of mental products in a form by which they may be transmitted 
to the mind through the eye, as spoken language communi- 
cates them through the ear. 

Written language may be either ideographic or phonetic. 
Ideographic writing may be either pictorial, representing 
objects by imitating their form, or symbolic, indicating their 
natnre or proportions. Phonetic writing may be syllabic or 
alphabetic ; in the former each character represents a syllable, 
in the latter an elementary sound. 

Origin of Written Language. — Of the origin of written 
language, but little is positively known. The Egj'ptians 
ascribed it to Thoth, the Grreeks to Hermes or Cadmus, and 
the Scandinavians to Odin. The first step toward writing 
was probably the rude pictorial representation of objects, the 
next step was the application of a symbolic signification to 
some of these figures. Pictures, abbreviated for convenience 
and by constant use, gradually became conventional signs ; 
and at last these characters became the S}' mbols of the sounds 
of spoken language. 

Systems of Written Ijanguage. — There have been four 
distinct systems of written language; the Ideographic, the 
Yerbal, the Syllabic, and the Alphabetic. These bear certain 
historic relations to each other, the last being an outgrowth 



NATURE OF LANGUAGE. 103 

of the first through the intermediate stages of the other two. 
A brief description "will be given of each. 

The Ideographic. — The Ideographic system {idea, idea, and 
grapho, I write), represented things by pictures and symbols. 
Concrete objects were iRdicated by their pictures, and abstract 
ideas by their S3>mbols, etc. Thus, the sun was indicated by 
a circle with a dot inside, 0, the moon, by a crescent, with a 
line inside,^ , a mountain b}- three peaks, side by side, \\\, 
rain, by drops under an overarching line, /f=^ , a child thus, 
J^ . These symbols could be combined to represent other 
objects. Thus loaler and eye combined represented tears ; 
an ear and a door represented hearing or understanding. 

Actions would be represented by objects in the attitude of 
the act, asjlying hy a picture of a flying bird, ascending by 
the picture of a person walking up a hill, etc. Some charac- 
ters were used symbolically, as a /tan*^ to indicate a ivorkman, 
two valves of a shell-fish to denote friends. Relations could 
also be represented, as above., by a dot over a horizontal line, 
heloio by a dot below a horizontal line, right by the symbol \ , 
and left by ^ , etc. These illustrations are taken from the 
Chinese system of written language. 

The system of writing among the Egyptians was hiero- 
glyphic, and is considered the finest of the kind. The sun 
with rays streaming from it, denoted light and brightness ; 
the moon, with its horns turned upward, denoted the month. 
Thej^ represented a siege by a scaling ladder, a battle by two 
hands, one holding a shield and the other an offensive weapon, 
ingratitude by a viper, p?'ow(Zence by an ej^e, etc. Two legs 
with the feet denoted movement, forward or backward, accord- 
ing to the direction of the feet, /^ or ^. The different emo- 
tions were indicated by the position of a man aflfected by them. 
Sometimes the sj^mbol is purely metaphorical, as when a king 
is represented by a bee, knoivledgehy a roll of -ptxnyrns, justice 
by the feather of an ostrich, because all the feathers of that bird 
were supposed to be of eqxial length. 



104 METHODS OF TEACHING. 

This kind of writing was very early used in Egypt and 
probabl}'^ in most of the ancient nations. It is the way in 
which rude races would naturally attempt to express their 
ideas by characters. In Mexico, when the Spaniards landed, 
intelligence was sent to Montezuma by paintings on cloth. 

The Verbal System. — The Yerbal System is that in which 
the spoken words of a language are represented by a symbol. 
This is but a stage of the Ideographic system. The charac- 
ters which were at first pictures or sj-mbols of objects, would 
in time become so modified that thej' would no longer rep- 
resent the object, but would be mere abstract symbols of 
objects and ideas. These abstract symbols, however, would 
represent, not the spoken words, but the objects and ideas. 
Thus, in the Chinese written language, which is largely verbal, 
each character has a name quite distinct from the name of the 
object represented by the character ; and children are required 
to learn the character and its name before the}'^ learn what the 
character, represents. But it is clear that people would, in 
time, begin to make an association between the character and 
the spoken Avord; and the ideographic sj^stem would thus 
become, to a great extent, verbal. 

The Syllabic System. — The Sjdlabic System is that in which 
the syllables of spoken words are represented by characters. 
This was a natural outgrowth of the ideographic and verbal 
systems. As soon as characters came to be used to represent 
spoken words, it would be noticed that manj'^ words consisted 
of similar parts, and the idea would occur of representing 
these parts by means of characters. Thus all such words as 
confer, contain, conscience, etc., would have a common char- 
acter to represent the first pai*t. 

It has been supposed that, at one time, all the Asiatic na- 
tions known to the ancients under the names of Syi'ians and 
Assyrians used the S3'llabic mode of writing.- The Cliiuese 
language is partly ideographic or verbal, and partly syllabic. 
In it there are 214 elementary signs or Leys,^\'\nc]i are strictly 



NATURE OF LANGUAGE. 105 

hieroglyphic, or abridged representations of visible objects. 
From these 214 elements, all the characters of the language 
(80,000, it is said) are formed by varying and combining 
these, every compound character representing one or more 
syllables having a distinct meaning. 

The Alphabetic System The Syllabic System would lead 

naturally to the Alphabetic System. Having analyzed oral 
words into syllabic parts, the next step would be to analyze 
syllables into their elements, and thus reach the elementary 
sounds of the language, which would be represented by char- 
acters. In adopting characters for the elementary sounds, it 
would be natural to select some of those which were already 
in use in the ideographic or syllabic system, taking those 
which stood for words or syllables approximating the element- 
ary sounds. For example, the Egyptian word, Ahom, signi- 
fied an eagle ; the figure of an eagle, therefore, stood, it was 
said, for the letter A, with which the word begins. B was 
represented by a censer (Berbe) ; R sometimes by a mouth 
(Ro), sometimes by a tear (Rime). An alphabetic system of 
w^riting had in this manner sprung up in Eg3^pt (the hiero- 
glyphics are partly alphabetic), but it was too imperfect to 
become an instrument of popular literature, and some have 
supposed that the Phoenician alphabetic system was formed 
out of the Egyptian system. 

III. Course in Language. 

Instruction in language includes eight things ; Learning to 
Talk, Learning to Read, Pronunciation, Orthography, Read- 
ing, Lexicology, Grammar, and Composition. There are 
some other divisions, but these ai-e all that are taught in the 
ordinary public schools. 

Learning to T(ilh\ — The child usually learns to talk at 
home before it is sent to school. Its teachers are its parents 
and the other members of the household. It learns by imi- 
tation and the principle of association. It hears words used 



106 METHODS OF TEACHING. 

and makes an association between them and. the objects or 
ideas for which they stand, and finally' imitates them in its 
attempts to talk. 

This work being done out of the school-room, does not fall 
within the province of the teacher, and will not here be dis- 
cussed. Much, however, might be said in advising parents 
to teach their children to talk correctly and with elegance. 
Culture of this kind is of the utmost value to the child. 
Habits of speech acquired in early chiklhood from parents 
and companions, stick to us through life and are often a 
blemish to high scholarship. Parents cannot be too careful 
in this respect. Aristotle obtained his elegance of language 
from his mother, and Alexander, it is said, never recovered 
from the bad habits acquired from Leonides, one of his earl}' 
teachers. 



CHAPTER II. 

TEACHING A CHILD TO READ. 

A CHILD'S first lesson in language is Learning to Talk. 
This it receives in the hallowed precincts of home, where 
the mother is the teacher. A child's first lesson in language, 
upon entering school, is Lear'ning to Bead. The teacher's 
first work, therefore, is to teach the child to read printed lan- 
guage. In this chapter we shall consider the methods of 
teaching a child to read. 

The pi'ocess of Learning to Read consists in learning to 
recognize written signs, and in associating spoken words with 
them. It embraces two things ; first, the learning of sight sym- 
bols, and second, the associating of sound S3'mbols with them. 
The basis of learning to read is, therefore, oral language. 

From this consideration, several principles arise: 1. The 
child should not begin reading until it is quite familiar with 
spoken language ; 2. In learning to read, there should be a 
transition from spoken to written word signs; 3. The first 
reading lessons should deal with familiar objects, actions, 
qualities, etc. ; 4. The reading lessons should begin with words 
and pass to sentences, as a child leai-ns to talk. To these may 
be added another principle, that the written word shall be 
regarded as the expression of the oral word, as the oral word 
is regarded as the expression of the object or idea. 

I. Methods of Teaching. — There are several methods of 
teaching a child to read. The most prominent of these are 
the Alphabetic Method, the Word Method, the Sentence 
Method, the Phonic Method, and the Phonetic Method. All 
of these have been practiced, and nearly all of them are still 
used, and have their advocates. 

(lOT) 



lOS METHODS OF TEACHING. 

TJie Alphabetic 3IefIioff. — The Alphabetic Method begins 
by teachinir the child the names of the letters. When these, 
or a snfiicient number of them, have been learned, the child is 
taught to pronounce words hy means of these names. This 
method, until within a few j^ears, was universall}'^ employed ; 
and it is still more largely used than any other. It is objec- 
tionable, however, and should be discarded. The objection 
is, that the word is not a S3aithesis of the names of the letters, 
neither do the names suggest the pronunciation of the word. 
The subject will be more fully discussed under pronunciation. 

TJie Word Method. — The Word Method begins by teach- 
ing words as wholes, without regard to the letters which com- 
pose them. Among the first to use the Word Method was 
Jacotet (1770-1840), a French philosopher and teacher; the 
most prominent advocate of it in this country is Prof. Webb, 
and by many it is known as the Webb method. In England 
it is popularly known as the " Look and Say" method, or as 
the method of " Reading without Spelling." 

This is undoubtedly a correct method with which to begin 
the subject. It is reallj^ the way in which pupils taught by 
the previous method actually learned to recognize words, for 
when a child spelled a word by calling its letters, he knew no 
more about its pronunciation than he did befoi'e he spelled it. 
The teacher gave him the name of the word, and when he for- 
got it, named it again and again, until he made a permanent 
association between the sound sj-mbol and the sight symT)ol, 
and thus remembered its name. 

The Sentence 3Iethod, The Sentence Method is tliat 

which begins with sentences instead of letters or separate 
words. By it the child's attention is called to some thought 
orally expressed, and then the written expression for this as a 
whole is presented and taught. The reason given for this 
method is "that the sentence is the unit of language," and 
that we read by sentences rather than by words. It is also 
claimed that pupils taught in this wa}^ read with more ease 



TEACHING A CHILI) TO READ, 109 

and with greater naturalness of expression. It is said that 
in order to read well, the eye must be kept in advance of the 
voice, which this method requires. 

There are several objections to the sentence method. First, 
it does not begin at the unit of language, which we believe to 
be the word rather than the sentence. Second, pupils taught 
b}^ this method very soon recognize the separate words, and 
consequently read by words rather than by sentences. Third, 
it is impossible that all or even a very large number of sen- 
tences can be taught in this wa}-, and eA'entuall}^ the child 
must come to the learning of separate words, in order to learn 
to read. Since word-reading must be learned and used, it 
seems best to begin in this wa}-. 

The Phonic 3Iefhod. — By the Phonic Method pupils are 
taught to pronounce words by combining the elementary 
sounds represented by the letters. It begins by teaching the 
elementary sounds and the characters which represent them. 
It uses the twenty-six characters of the alphabet to represent 
twenty-six sounds, and then employs a notation to indicate 
the remaining sounds. It also indicates the silent letters of 
words by printing them in italics or a different-faced type. 

The Phonic Method is, beyond question, the correct 
method of teaching pupils to pronounce words. It is natural 
and simple, and enables a pupil to pronounce a new word in- 
dependently of the teacher. In connection with the Word 
Method, it is the true method of teaching a child to read. It 
will be discussed moi'e in detail under Pronunciation. 

Tfie Phonetic Method. — The Phonetic Method is in princi- 
ple similar to the Phonic Method. It begins by teaching the 
elementary sounds and the characters which represent them. 
It uses the twenty-six letters of the alphabet to represent 
twenty-six sounds, and then invents other characters to rep- 
resent the remaining sounds. It spells the words as the}'' are 
pronounced, using only as many characters as are sounded, 
and requires the pupil to make a transition from the phonetic 



110 METHODS OF TEACHING 

form of the word to the ordinary form. It will be further 
considered under Pronunciation. 

II. The True Method. — Having stated the sevei-al methods 
by which a child may be taught to read, we proceed to describe 
what we regard as the con-ect method in practice. The true 
method consists of a combination of the Word Method and 
the Phonic Method. We should begin with the Word Method, 
and after the child becomes familiar with a number of words, 
and can read little sentences, we should analyze the words 
into their elementary sounds and characters, and thus connect 
with it the Phonic Method. 

The Word Method. — The True Method begins with words. 
The proper place for a child to begin to learn to read is not 
with the letters of a word, but with the word itself. The rea- 
sons for this are many, a few of which will be stated. 

First, the Word is the Unit of language. Language begins 
with words, not with letters or sentences. Letters are the 
fractions of written words, and we should not begin with frac- 
tions. Sentences are the syntheses of linguistic units, and the 
units should precede their combination. Second, it coincides 
with the manner of learning oral language. The child begins 
language with spoken words, and not with their elements, 
the elementary sounds. It would be as sensible for a mother 
to teach her child to talk by beginning with the elementary 
sounds, as for one to teach a child to read by beginning with 
the letters. 

Third, it is in accordance with a fundamental principle of 
teaching, from the known to the unknown. We begin with the 
spoken word which is known, and pass from it to the unknown 
written word. To begin with the letters, is to deal entirely 
with the unknown, as these abstract and arbitrary symbols 
cannot, except in a few instances, be associated with anything 
known. Besides, the method of beginning with words is 
much more interesting to the child, as in a few lessons he is 
reading little sentences which he understands. 



TEACHING A CHILD TO READ. Ill 

Fourth, to begin at the word as a whole, and pass to its 
parts, proceeds by analysis, which is the natural wa}'' in which 
a little child acquires knowledge. It knows a norse or a tree, 
not hy beginning with their parts and uniting them into one 
complete object, but by first knowing them as wholes, and 
subsequently becoming familiar with their parts. The natu- 
ral law of instruction is from the whole to the parts ; first 
analysis and then synthesis. 

For one who has not used this method, it is natural to think 
that a child cannot know a written word without knowing the 
lettei's which compose it. This, however, is a mistake. We 
do not analyze a word into its letters when we read, any more 
than we analyze an object, like a horse, into its parts, in order 
to be able to know what it is. We know the object as a whole, 
at a glance, and remember its name ; so we know a word by 
its general appearance, just as we know a picture or an object. 
It stands before the mind as a picture of an idea or of a 
spoken word. 

It may also be objected that all words cannot be learned in 
this way; and that the pupil acquires no power to pronounce 
independently of the teachei*. The same objection applies to 
the alphabetic method, from whose advocates this objection 
is liable to come. The fact is, that both should be followed 
by the phonic method, by which a pupil may learn to pro- 
nounce independentl}'^ of the teacher. 

The method, however, becomes more than a " look and sa}^" 
method to the learner. The child soon begins to make com- 
parisons, and discover analogies which aid him in pronuncia- 
tion. The teacher may advert to no principle of sound, but 
the child does so spontaneously and unconsciously. The as- 
sociation of sound with sign which he makes in one word, he 
endeavors to apply in other analogous words, as any one will 
notice who observes carefully. He thus learas to pronounce 
many words independently of the teacher, as he does in 
using the alphabetic method. 



112 METHODS OF TEACHING. 

The First Step, therefore, in teaching a child to read, is to 
begin with the written word, as tlae child begins spoken lan- 
guage with th5 spoken word. The first lesson is a lesson on 
printed words. We should begin with some familiar spoken 
word which the child knows, and then pass to the written 
word, and make it known. We teach a few words in this way 
and then unite them into sentences, and have the child read 
little sentences. After he has been reading several days, or 
a few weeks, if the teacher prefers, we should pass to the 
Phonic Method. 

Phonic 3Iethod. — The Second Step is to pass to the elements 
of words. As there are two classes of words, oral and written, 
so there are two classes of elements of words. The elements 
of SY)o\i.en \YOYds are the elementa?vj sounds ; tlie elements of 
written words are the letters. 

It has been a question which elements we should present 
first, the sounds or the letters; but it is a question easily 
answered. Since we learn spoken words before written words, 
we should first analyze the spoken words into their elements, 
and subsequently teach the characters which represent them. 
By analyzing a word, as cat, we show the pupil that a spoken 
word consists of distinct sounds ; we then teach him to make 
these sounds, and afterward teach the characters which rep- 
resent them. In this way the letters are introduced as sym- 
bols of sounds, and not as abstract characters with names. 

In presenting these characters, since some letters represent 
different sounds, it is necessary to introduce a system of no- 
tation to indicate the sound of those characters that represent 
more than one sound. This notation may be the figures 1, 2, 
3, etc., used as indices or subscripts, or the notation of the 
dictionar}'. In practice, it will be best to use the notation of 
the reader or speller used in the school. 

It is also necessary to indicate the silent letter's of words, 
so tliat pupils may know just what letters are to be sounded 
in pronouncing printed words. This can be done by printing 



TEACHING A CHILD TO READ. 113 

such letters in italics, as is the general custom, or in a lighter 
faced type, as in Dr. Leigh's method, or by printing them with 
a stroke across them, as is done in Appleton's series of 
readers. 

The Third Step is to require the pupil to pronounce words 
by combining the sounds of the letters which they see com- 
bined in the words. Thus, when he sees the word hat^ he 
knows the first sound is that of 6, the second a/i, and the third 
the aspirate t; and uttering these sounds in their order, he has 
the correct pronunciation of the word hat. Or, suppose the 
word is li(//it; he sees that g and /lare not to be sounded, and 
he gives the sounds of /", t, and ^, one after another, so that 
they coalesce, and he has the correct pronunciation of tlie 
word fight. The pupil, becoming familiar with the words 
printed in this form, will readily recognize them, and be able 
to pronounce them when printed in the ordinary form. 

Last of all, teach the names of the letters and their order in 
the alphabet. Should it be asked how soon the names of the 
letters should be introduced, we answer that if the pupils 
know the names of the letters by the time they have com- 
pleted the primer or primary reader, it is sufficient for all 
practical purposes. They have very little use for their names, 
and may distinguish them by their sounds at first. 

Model Lesson. — To illustrate, suppose we begin with a 
common word like cat. I ask some questions and talk about 
a cat. I then point to the picture of a cat on the card or in 
the book, and ask its name, which the pupils give me. I then 
call attention to the fact that all these sounds which we make 
when we talk are called ivords. I then lead them to notice 
that the words which they know are those which they hear. 
I then tell them that there are also words which they can see, 
and awaken an interest to know such words. I then point 
out the word cat on the card or in the book, and tell thera 
that it is the visible or written word cat. In the same way I 
teach the written words that represent other objects. 



114 METHODS OF TEACHING. 

I next teach written words that are not the names of 
objects. I have the pupils sa}' something about an object ; as, 
"I see a cat," and then show them this sentence on the card 
or in the book, or I print it on the board ; and then teach 
them each word of this sentence. I do the same with other 
sentences, making use of some of the words already- learned, 
and proceed thus as far as I deem it advisable. In this vfixy 
I pass from audible speech to visible speech. 

After the pupils have learned quite a number of words and 
read several pages in their primer, I proceed to the analysis 
of words into their elements. To give them an idea of the 
elements of words, I first take some object, as a knife^ and 
lead them to see that it consists of parts. I then take some 
oral word, as cat^ and pronouncing it slowly, separate it into 
its three phonetic elements, the sounds of c,a^ and f, and let 
them hear that this word consists of three distinct sounds. I 
then have the pupils give these elements, imitating the sounds 
as I make them. I then teach them the letters (not their 
names) c, a, and t, which represent these sounds. I then 
have them unite these sounds in succession, as they see the 
letters united in the word, and thus pronounce the word. I 
proceed in the same way with other words and sounds until 
the pupils can pronounce words quite readily. 

As the different sounds of the same letter are presented, we 
must introduce a notation to indicate the sound of the char- 
acter, and also show how the silent letters are represented. 
TJse at first, also, only words of simple and regular formation, 
omitting such words as tongue, thought, knife, etc. 

General Suf/f/esHons. — We should teach the short sounds 
of the vowels first, as a in a/, e in en, i in in, o in on, u in us; 
and the simple consonants, as b, d, /, I, vi, n, p, etc. We 
should then drill the pupil in pronouncing their combinations 
in words of two letters, as an, at, in. ox, etc. Then words 
of three letters may be given, as fan, bat, bit, box, fox, etc. 
We should then introduce some of the other sounds of the 



TE.VCHIXG A CHILD TO READ. 



115 



vowels, as d, e, i, o, etc.. indicating them by the pi'oper nota- 
tion, and combine these with the characters already given. 
Next show how silent letters are represented, and introduce 
such words as caiiR, rate, fate, mate, fine, line, etc. 

The teacher may use the blackboard in teaching pronuncia- 
tion with great advantage. Let him print the letter a on the 
board, and have the pupils give its sound ; then place the 
letter t after it, and have the pupils give its sound, and also 
the sound of the combination at; then place the letter b at the 
left, have the pupils give its sound and the sound of the com- 
bination bat. Then erase the b and substitute each of the 
consonants /, r, 7?i, n, s, and v in its place, and require the 
pupils to pronounce the word. A similar exercise may be 
had on other combinations. 

To aid the pupils in learning new words, columns of similar 
words may be written on the board so that the pupils may see 
their pronunciation partly by the analogy of words. Thus: 



cat 
rat 


in 
tin 


car 
far 


ten 
hen 


bit 

fit 


gun 
fun 


hat 
fat 


pin 
fin 


tar 
mar 


pen 
fen 


pit 

sit 


run 

sun. 



They may also be arranged so that the common element 
may be seen and readily joined with the different single ele- 
ments. Thus, take the comVnnations af, an, o^, ogr, and i7?, 
which we suppose the pupils have learned, and combine them 
with the different consonants, as is indicated below. 



at 



Classes of words may also be selected which have the com- 
mon element first, as, cat, can, cap, cab, etc. These words 
could be grouped in books or on cards, or may be printed on 
the blackboard. The method of using such exercises is so 
evident that we need not describe it. It is remarkable how 



b-at 


' c-an 




'c-ot 


'b-og 




fb-ill 


c-at 


f-an 




h-ot 


c-og 




h-ill 


f-at an \ m-an 


ot \ 1-ot og < 


d-og 


ill< 


m-iU 


h-at 


p-an 




n-ot 


f-og 




t-ill 


r-at 


r-an 




p-ot 


1-og 




k-ill 



116 METHODS OF TEACHING, 

soon children acquire the sounds of letters, both consonants 
and vowels, and when this is done, they have the key to 
reading in their hands. 

It would be well to have words arranged in columns in the 
reader or spelling-book, classed according to their analogies of 
sound, with the character or combination of characters used 
to represent the sound placed at the head of the lesson to 
serve as a key to the pronunciation. Thus a, as in late^ would 
indicate the sound of such words as aiin^ they, nail, steak, 
gauge, etc, ; or sh in ship would be the key to the pronuncia- 
tion of words which contain the combinations ti, si, ci, ch, ce, 
se, sch, etc. 

The pupil should also have plenty of exercise in forming new 
words by combining the sounds of the characters as already 
explained. The small letters are, of course, to be taught first. 
The pupils should be required to print the letters and the 
words on their slates and on the blackboard. 

After the pupils have learned to read by the word method 
and the phonic method, I should have them name the letters 
of words, and pronounce the words. This was the old method, 
and pupils will find it convenient to be able to name the letters 
of words, though the names of the letters will not enable them 
to pronounce the word. 

It will thus be seen that the true order of teaching a child 
to read is, — first, the object or idea ; second, its sound symbol, 
or spoken word; third, the form symbol, or printed word; 
fourth, the elements of the spoken word, or the elementary 
sounds; fifth, the elements of written words, or the letters 
representing the elementary sounds; and, sixth, the synthesis 
of these sounds, as the pupil sees the letters united in the 
printed words. Subsequently, the pupil ma}^ be taught to 
represent the words b}^ writing them on the slate or black- 
board. This is the true, simj^lo, and natural method ; and tliis 
order of learning to read the language will correspond with 
the order of using it. Words, then, will become as mirrors 



TEACHING A CHILD TO READ. 117 

reflecting objects and ideas to the minds of pupils. Sense and 
sounds and form and use, will become so intimately blended 
together that pupils may easily be led to use conversational 
tones in reading, and a natural style of expression will follow 
as a natural result. 

In this work of instruction, the teacher may use Books, or 
Heading Cards, or the Blackboard. Each one of these has 
its own peculiar advantages ; and in actual instruction it will 
be best to combine the use of them all. Every primar}- school 
should be supplied with a set of Reading Cards, and the 
teacher should practice until he can print the words neatly on 
the board. The pupils should also be taught to print words 
on the slate and blackboard. They should also be taught the 
use of the script letters at as early a period as is convenient, 
and be required to use them in making and pronouncing- 
words. 



CHAPTER nr. 

TEACIIINa THE ALPHABET. 

IN" teaching a child to read, we have used the letters as rep- 
resenting sounds, though we have not called attention to 
their form or their names. The next step is to make a child 
familiar with the forms and names of the letters. Since some 
knowledge of the origin and nature of the alphabet will be 
interesting to teachers, we shall divide this chapter into two 
parts; the Nature of the Alphabet and the Methods of Teach- 
ing the Alphabet. 

I. The Nature of the Alphabet. 

Definition.. — The Alphabet is a system of characters used 
to represent the elementary sounds of a language. The term 
alphabet is dei'ived from alpha and beta^ the first two letters 
of the Greek alphabet. It comes to us from the Latin alpha- 
betum^ which, howcA^er, it is said, occurs in no prose writer 
before TertuUian, though it is presumed that the word had 
previously existed. 

Or iff in. — Our alphabet was derived from the Latin, which 
was derived from the Greek, which, it is supposed, was derived 
from the Phoenician, or from the Hebrew, with which it is 
closely allied. It is said that Cadmus, 1500 B. C, brought 
IG letters into Greece; Palamedes subsequently added 4, and 
Simonides 4 more, which accounts for the 24 letters of the 
Greek alphabet. 

The forms of our alphabetic characters are derived from the 
Phoenician letters. The origin of these primitive forms is not 
positively known. It has been supposed, but without author- 

(118) 



NATURE 'OF THE ALPHABET. 119 

ity, that they originally represented the shape of the mouth in 
making the sound. It is now generally believed hy those who 
have investigated the subject, that they are modifications of 
the system of hieroglyphics, or picture-writing, used in Egypt. 
The Phoenicians probably took the Egyptian characters, which 
were symbols of words, and changed them into symbols of 
sounds. 

Greeh Clianges. — In adopting the Phoenician alphabet, the 
Greeks made man}- considerable changes in the values of the 
symbols. Several of them were unnecessary, for they had no 
sounds in their language to correspond with them, and they 
were dropped. The Phoenicians had no proper vowels ; the 
Greeks therefore employed as such those letters which were 
nearest akin to voAvels; A, E, F, H, I, and 0. To the Phoeni- 
cian alphabet the Greeks added the aspirates $ and x, the 
double consonant i', and the sign for long o, Q, placing these 
new letters at the end. To distinguish these, the short o was 
called "0 uiKodv^ small o; and the long o^'^/iiya, great o. A few 
other changes were made, which we cannot here notice. The 
Greek alphabet, in its complete form, was first adopted by the 
lonians. It was first used in Attic inscriptions in the archon- 
ship of Euclides, 403 B. C. 

Latin Changes. — The Latins also introduced many changes, 
as ( 1 ) in the use of the symbol (F) vau., to denote not the 
V but the / sound, ^-hich was probably strange to the Greeks; 
(2) in allowing K. to fall almost out of use, and employing C 
instead; (3) in forming a new symbol G,r. e., C with a distin- 
guishing line, to mark the soft gutturals, about the od cen- 
tury B.C.; ( 4 ) in the addition, in the 1st centuiy B. C, of the 
two symbols Y and Z after X (which had long been the last 
letter of the alphabet), to express the Greek sounds v (upsilon) 
and z (zeta). 

English Changes. — The alphabet, as derived from the 
Latin, has been somewhat modified in the English language. 
Thus I and J, which were at first merely graphic variations, 



120 METHODS OF TEACHING. 

were cliauged by the Dutch printers during the 16th and 17tli 
centuries, to represent different sounds. The lettei's U and Y, 
which were formerly used indiscriminately to represent the 
same sound, acquired separate uses about the same time. AV 
Avas added some time during the Middle Ages. It is a com- 
bination of two Vs, the letter v being formerly called u, which 
accounts for the name " double u." 

Oider of Characters.— When, by whom, and why the let- 
ters of the alphabet were arranged as we now have them, 
cannot be explained. The present arrangement has given rise 
to much ingenious speculation. It has b«en supposed b}- 
some that there are traces of regularity in the present order. 
Thus, the three soft momentar^^ sounds b, g, d were placed 
together; p, k, and t may have once been together and sepa- 
rated by later intrusions; /, m, and n have an affinity indi- 
cated b}^ the name liquids, etc. It is hardly probable, how- 
ever, that the symbols were arranged upon any scientilic 
method; but that chance guided the general arrangement, 
though a few sounds obviously similar maj^ have been put 
together intentionally. 

Karnes of Letters. — The Romans also changed the Greek 
names for the characters of the alphabet. The vowels were 
known b^^ their sounds only. The momentarj^ consonants and 
/(. were denoted by their own sound followed by a vowel; as, 
be, ce, de, ge, pe, and te, and also ka and ha; q had sufficient 
vowel sound to float it alone ; on the other hand, the continu- 
ous consonants were preceded by a vowel; as, ef, el, em, er, 
es ; and x was called ix. 

This difference in the method of naming the consonants was 
obviously caused by their nature. Momentary sounds, are pro- 
duced by a complete closure and opening of the organs re- 
quired in each case ; when this opening is made, the organs 
are so placed as to form a vowel, which is naturally produced 
by the remnant of sound required for the consonant ; whereas 
a vowel (lannot be i)r()du(!ed before ;iny one of these sounds 



NATURE OF THE ALPHABET. 121 

without conscious effort ; hence it is simpler. to call A?,/;a, than 
to call it ak. The continuous sounds, however, are produced 
with the organs slightl}^ open, in which ease a certain amount 
of vowel sound tends to escape just as the organs are drawing 
together to produce the consonant, and is thus heard before 
it; but to sound a vowel after one of these consonants, the 
organs must intentionally be put in the proper position. 
Thus, the same principle — the conscious or unconscious striv- 
ing for ease of articulation — produces opposite results in the 
case of the momentary and continuous consonants. 

The same principle caused a different vowel to be used for 
h and k^ from that which is used for the other letters. In 
sounding the letter a (ah), the organs are in nearly' the same 
position as in sounding these two gutturals, only a little more 
open ; whereas the position for sounding e («.'/) is more nearly 
that of all the other consonants. The sound of e, as here used, 
is ay, and of a, is a/i, which, it is supposed, was the Latin sound ; 
thus a Roman would have spoken of learning not his a-bee-see, 
but his ah-bay-kay. 

Clnssi/icafion. — The letters of the alphabet have been clas- 
sified with respect to their historj^, as follows : (1) B, D, H, 
K, L, M, N, P, Q, R, S, and T, letters from the Phoenicians ; 
(2) A, E, I, O, Z, originally Phoenician, but changed by the 
Greeks ; (3) U (same as V) and X, invented by the Greeks ; 
(4) C and F, Phoenician letters, changed in value; (5) G, of 
Ijatin invention ; (6) Y, introduced into Latin from the Greek, 
with changed form ; (7) J and Y, graphic Latin forms varied 
to independent letters ; (8) W, a recent addition, formed b}' 
doubling U or Y, whence its name. 

Cfijf if als and Small Letters. — In ancient Greek writing, 
the capital lettei'S were principally used, and with no division 
marked between the words. The small cursive character was 
introduced during the eighth century, though the introdugtion 
must have been gradual ; for, in the oldest Greek manuscripts, 
even as early as the fifth centurj', they appear intermixed with 
capitals. 



122 METHODS OF TEACHING. 

Vowels and Consonants. — .The Phoenician alphabet con- 
sisted of 28 letters, none of which were vowels. They em- 
ployed hardly any vowel signs. In Hebrew, the three princi- 
pal sounds, a, t, it, were sometimes expressed in writing, and 
long i and u were denoted, not by special signs, but by con- 
sonants akin to them ; a was regularly omitted except at the 
end of a word, whei-e it was denoted by He, and sometimes by 
Aleph. In fiict, in all Semitic languages, the practice was to 
ignoi-e vowels in writing, leaving it to the reader to fill, ac- 
cording to the context, the unvarying framework of conso- 
nantal sounds. The Hebrew vowel points were a later invention, 
rendered necessarj^ when the language ceased to be spoken. 

Direction of Writing. — The direction of writing varied 
among the different nations of antiquity ; but in general the 
Semitic races wrote from right to left and the Aryan from left 
to right. The early Greeks, like the Phoenicians and other 
eastern nations, originally wrote from right to left. Subse- 
quently they wrote consecutively from right to left and left to 
right, as land is plowed, the writing being called farroioed 
luriting. This method was continued for a long time; the 
laws of Solon, promulgated 594 B. C, were written thus ; and 
it was used until the fifth century B. C. Writing from left to 
right was introduced, however, before the alternate method 
was abandoned ; inscriptions dated 142 B. C. have been found 
written from left to right ; and Herodotus speaks of the 
method of writing from left to right as the established cus- 
tom of the Greeks in his time. 

The Chinese and Japanese write in columns, beginning at 
the top and passing from right to left. The Mexican picture- 
v>rriting was also in columns, and read from the bottom 
upward. The Egyptian hieroglyphics are sometimes without 
any arrangement, but are generally written either in columns 
or horizontal lines, according to the shape of the surface to be 
inscribed. The cuneiform inscriptions are always from left to 
riglit. 



teaching the alphabet. 123 

11. Methods op Teaghixg- the Alphabet. 

After pupils have learned to read little sentences, and have 
analyzed spoken words into their elements, the elementary 
sounds, and written words into their elements, letters, these 
letters and their names are to be taught; and we will now 
proceed to consider the ways in which it may be done. 

It will be noticed that there is a difference between knowing 
the letters and knowing their names. In teaching children 
the sounds of the letters before their names, they will have 
become fiimiliar with the forms of the letters before they know 
what to call them. Indeed, if they were asked their names, 
they would no doubt give the sound of the letter as the name 
of it. 

.The Methods. — The alphabet may be taught with a Book, 
with Cards, and with Slate and Blackboard. Each of these 
methods has its advantages, and they may all be used bj'' the 
teacher. 

With a Book. — The old method of teaching the alphabet 
was to begin at A and, the teacher pointing with a knife or 
pen, have the pupil go all the wa^^ down to Z, and then go 
back again up 'to A. Sometimes there would be a little 
" skipping around" among the letters, and occasionally, an 
effort made to fix some particular letter in the memory of the 
child. Two such lessons in the forenoon and two in the after- 
noon constituted the entire work of the primary pupils in our 
public schools thirty or foi-ty years ago; and it is said that 
this method is not yet obsolete. It often required several 
months for the pupil to learn all the letters when taught by 
this method. Pupils were frequently known to be able to 
repeat all the names of the letters in their order without know- 
ing the letters to which the names belonged. 

The correct method, in teaching with the Book, is to select 
some of the most easily remembered forms, as o, .x, i, etc., call 
attention to the peculiarities of their form, and thus impress 



124 METHODS OF TEACHING. 

them and their names on the memory. Teach a few letters 
the first day, review these and add a few more the next day, 
and thus continue until all are learned. In this way the entire 
alphabet can be taught in a very few days. 

An advantage of the pupils having books is that they may 
have them at their seats, and look at the letters when not re- 
citing, and thus become familiar with their forms. They may 
thus also print the letters from their books on their slates, 
which will impress their forms. Another adA^antage is that 
they may take their books home and get some instruction 
from their brothers and sisters or their parents. An objection 
to the use of the book, as compared with the use of cards, is 
that it does not admit of classification; onl}' one or two can 
thus recite at a time. 

With Cards. — We may also teach the alphabet by the use 
of Cards. To teach by this method we need a set of cards. 
These cards should be large, containing letters printed on 
them in large type. The first card of the set should have 
some of the more easily learned letters, as O, X, S, etc., 
printed near its centre, and the same letters in connection 
with others in the margin. The next card should contain 
more new letters in the centre, and these and those already 
learned be combined with others in the margin. The letters 
should also be combined in words, both near the centre of the 
card and in the margin of it. 

The teacher will call attention to some letter, as o, talk 
about it, awaken an interest to know its name, and then give 
the name and have the pupils repeat it. Do the same with 
another letter and another, until he has taught as many in one 
lesson as he thinks the pupils can remember. He may theni 
send some one to the card to point out tlie letters as he names 
them ; or he may have the class name them as he points thorn 
out. 

He may then have the pupils search for some of the letters 
in the margin of the card where they are mixed with other 



TEACHING THE ALPHABET. 125 

letters. A little competitive trial of skill maj" be had to see 
who will find the most letters in the margin. Such an exercise 
Dr. Wickersham describes under the head of " hide and seek" 
with letters. A high degree of interest can be aroused in this 
way. 

The advantage of the Card Method is that it admits of clas- 
sification. A dozen or more can recite at the same time. It 
also excites a deep interest on account of its allowing a com- 
petitive trial, which makes the lesson attractive and aids in 
fixing the forms and names in the mind. It has the disadvan- 
tage, compared with the Book Method, of not being accessi- 
ble to the children at their seats or at home. It should be 
used in connection with the book method. 

Slate and Ulachhoard. — The Slate and Blackboard may 
be used in teaching the alphabet. In teaching the letters in 
this way, the teacher should go to the board and print the 
letter neatly upon it ; and, calling attention to the peculiarity 
of its form, as before suggested, show the pupils how he makes 
it, and give them its name. He should then require the pupils 
to make the letter upon the slate or blackboard, correcting 
their errors, and showing how to improve its form. He 
should proceed in this way with all the letters, beginning as 
before with the most easily remembered. 

There are several letters which it is difficult for pupils to 
distinguish from one another, that ma}^ be best taught by this 
method. The principal of these, among the small letters, are 
6, cZj-p, and q. These letters may be divided into two parts, 
called the curve and the stem. The teacher may draw a stem 
on the board, and put the curve first in one place, and then 
another, now at the lower right hand corner, then at the lower 
left hand corner, etc., requiring the pupil to give the name of 
the letter thus formed. The blackboard can also be advanta- 
geously used in teaching pupils to distinguish such letters as 
c and e, n and it, etc. 

One advantage of the slate and blackboard method is that 



126 METHODS OF TEACHING. 

the drawing of the form impresses the form on the mind. 
Another advantage is that it affords pleasant emplo3^ment for 
the pupils when at their seats. In order to have them draw 
when not reciting, tlie teaclier may print large letters on the 
board for them to copy, or they may copy from their cards or 
their books. 

General MeinarliS. — Children at home may have blocks 
with the letters on them ; but these will not be found very con- 
venient in a public school. A Reading Frame, consisting of 
an upright frame on which strips are fastened, forming grooves 
in which blocks containing letters may be placed, is also 
recommended, and ma}^ be used in a primary school with ad- 
vantage. It is not needed, however, in an ordinary public 
school. 

Should the small letters or the capitals be taught first? The 
old custom was to teach the capitals first ; but it is now 
thought that the small letters should be taught before the 
capitals. This is almost a necessity, if we teach pupils words 
before letters, and analj^ze words into their letters, as words 
in their ordinary form are printed in small letters. But even 
if letters were taught before words, the small letters sliould 
be taught first, since we should immediatel}' unite the letters 
into words. Besides this, when pupils are taught the small 
letters, they will learn the capitals almost without any instruc- 
tion. 

Finally, remember that the pupils should be taught to re- 
peat the letters in their proper order. This will be needed in 
consulting the dictionary, and for man}'' other purposes. 



CHAPTER ly. 

TEACHING PRONUNCIATION. 

T)RONUNCIATION consists in the correct utterance of 
J- words. The term jji^onunciation is derived from _p?'0, 
forth, and nuncio, I announce; and means, literally, a speak- 
ing forth. 

Words may be pronounced upon seeing the characters 
which compose them, or upon hearing uttei-ed the names of 
the cliaracters, or the sounds represented by the characters. 
In reading, we pronounce words upon seeing the characters 
Avhich compose them. If the letters of a familiar word be 
named to us in their order, or if the sounds of any word be 
thus given, we can pronounce the word. 

I. Nature and Importance. 

Tbe pronunciation of the English language, like that of all 
living languages, is in a great measure arbitrary. It. is liable 
to change from one ago to another ; and varies in different 
countries where it is spoken, and in different divisions of the 
same country. Even people of the same place differ in the 
pronunciation of many words, influenced by the caprices of 
fashion and taste. 

The standard of pronunciation is the present usage of lite- 
rai-y and cultivated society. In England, the usage of the 
best society of London is regarded as the principal standard, 
though the usage of good society in that city is not unifoi'm. 
We have no one city in this country which holds a correspond- 
ing rank as a centre of intelligence and fashioji, and thus no 
special standard of usage to govern us. American scholars 
are, however, largely influenced by English custom. 

(127) 



128 METHODS OF TEACHING. 

A standard dictionary should aim to present the best usage 
of the present time. The standard, therefore, for students, is 
the standard dictionary. The standard dictionaries of this 
country are Webster and Worcester. Where they agree, we 
have a guide which we may follow with entire confidence. 
Where they differ, we must decide by the custom of the best 
speakers that we hear, or by other information that we may 
possess. Of course, we have excellent avithority for our usage, 
if we follow cither one of these dictionaries. 

It is a good rule not to differ from those with whom we as- 
sociate any further than correct usage actually requires. It 
seems like an affectation to use a pronunciation different from 
our associates, when theirs is also supported by good author- 
it3\ For an American to say either (ither) and neAther 
(ni they-) in society when these words are pronounced accord- 
ing to the usual cu.stom e ther and ne ther, is an inexcusable 
affectation. We should always remember, also, that though 
our own pronunciation is right, another person's may not be 
wrong when it differs from ours. The pronunciation of words 
is not a matter of absolute right, but of taste and culture. 

The pronunciation of the English language is very difficult. 
This difficulty arises partly from the irregularity^ of our or- 
thography, and partly from the carelessness of persons in 
respect to pronunciation. Many persons pronounce incor- 
rectly a large number of the words they use in ordinary con- 
versation ; and very few persons can read a page of an ordi- 
nary book without several mispronunciations. Indeed, it is 
an exceptional thing to listen to a public speaker tvho does 
not make many mistakes of this kind in an hour's address. 

The correct pronunciation of words does not receive the 
attention which its importance demands. Men who would 
blush at a mistake in grammar, or feel deeply mortified at the 
misspelling of a word, go on, year after year, mispronouncing 
many of the ordinary words, with apparent indifference, and 
with no effort at correcting their mistakes. Such mistakes as 



TEACHING PRONUNCIATION. 129 

i'dea for ide'a^ complex' for com'plex, in'quiry for inqui'ry^ 
and the incorrect sounds of the vowel in such words as food^ 
roQt, half, jmst, etc, we hear constantly made by educated 
men, who thus show their lack of literary culture and refine- 
ment. 

Correct pronunciation is of even greater importance than 
correct spelling, since we make constant and dailj' use of 
spoken words, while we write much less frequently. A mis- 
spelled word is an offence to the e^^e, but a mispronounced 
word is an offence to the ear ; and the ear is as delicate and 
refined as the e3^e. It sliould be regarded as less displeasing 
to see a misspelled word in a person's letter than to hear a 
mispronounced word in his conversation or speech. 

Teachers should be especially particular in respect to pro- 
nunciation. They should be careful that they pronounce cor- 
rectly'' as a model for their pupils to imitate. They should 
make constant efforts to correct the mistakes of their pupils, 
and to train them to pronounce correctly. It is not sufiicient 
that attention be called to their mistakes ; but pupils should 
be drilled on the mispronounced words until they have 
acquired the habit of pronouncing them correctly. Pupils 
should be required to keep a list of the words which they mis- 
pi'onounce, and be frequently drilled upon them. 

II. Methods of Teaching. 

There are two distinct methods of teaching the pronuncia- 
tion of words, called the Associative Method and the Phonic 
Method. Both of these have already been referred to in teach- 
ing a child to read; they will now be discussed more fully. 

The Associative 3Iethod. — The Associative Method con- 
sists in teaching the pronunciation of words by leading the 
pupil to associate the name of the word with its form. This 
is the method by which we begin to teach a little child to read. 
The pupil sees the word, the teacher gives its name, and the 
6* 



130 METHODS OF TEACHING. 

pupil is required to associate tlie name with the form and 
remember it, just as he learns the name of any other object. 
In this way a child learns to pronounce words before it knows 
its letters. 

This is the correct method for the beginner. First, it is the 
natural method ; it is the same way in which we begin spoken 
language, and in whicli we learn the names of other objects. 
It is also the most interesting method ; for a young pupil is 
more interested in words than in abstract characters. It is 
the most philosophical method, for it proceeds from the 
known to the unknoivn, from the known spoken word to the 
unknown written word. It is also the historic method; for 
written language employed symbols for entire words before 
it used letters ; and the liistorical order of development gen- 
erally indicates the true order for the child. 

The associative method, however, has its limitations. The 
pupil can pronounce only the words which have been pro- 
nounced for him. Each new word must be named for him 
before he can pronounce it. He attains no knowledge by 
which he can pronounce new words independently of the 
teacher. It therefore needs to be supplemented by some 
other method by which the pupil can learn to pronounce new 
words for himself. This method is the Phonic Method, which 
we shall now consider. 

The Phonic MetJiod. — The Phonic Method of teaching 
pronunciation is that by wliich we teach pupils to pronounce 
words by combining their elementary sounds. By this method 
we first teach the pupils the elementar}' sounds, then the 
characters which represent these sounds, and then lead the 
pupil to combine the sounds in their order as he sees the 
letters. 

Were the English language phonetic, this method would be 
entirely simple and eas}'. Having learned the sounds and the 
characters representing them, the pupil would be able to pro- 
nounce, with a little practice, any word he might see. A Ian- 



TEACHING PRONUNCIATION. 131 

guage is phonetic wlien it has a character to represent each ele- 
mentary sound, when each elementar}^ sound is represented by 
but one character, and when words are spelled as pronounced 
and pronounced as spelled. The English language is not pho- 
netic ; hence this general method becomes somewhat modified 
in its application, and its difficulties are increased. We shall 
describe how the method ma}'^ be applied to our language. 

There being about fort}'' sounds in the language, and only 
twenty-six characters, we have not characters enough to rep- 
resent all the sounds ; we are therefore compelled to adopt 
some notation to be used with these characters to indicate the 
remaining fourteen sounds. We may use figures as exponents 
or subscripts, or the marks in some standard dictionarj^. 
Thus, a 1 or fflj , or a might repi'esent the first sound of a; a^^ox 
a 2, or a might represent the second sound of a; etc. The 
different sounds of the consonants ma}' also be indicated by 
marks. All the primary readers should have some notation 
which the teacher can adopt in this instruction. 

The next step in the method is to indicate the silent letters, 
so that the pupil may know, on seeing a word, what letters to 
sound and what not to sound. This may be done by print- 
ing the silent letters in a lighter-faced tj^pe as Dr. Leigh does, 
or in italics, as is done in many of our spelling-books and 
readers, or with a stroke across them, as is done in a recent 
series of readers. Thus the word/a^e might be printed fate 
or fate; the word light, light, or light. 

Having received this instruction, the pupil will be able, 
with a very little practice, to pronounce all new words that he 
meets in his readers. All that he must do to pronounce a 
Avord is to give the elementary sounds, as indicated by its let- 
ters, in the order in which they occur in the word, being care- 
ful that the}' flow, naturally and musically into one another. 
After he is familiar with words printed in this way, he will 
experience little difficulty in recognizing them when printed 
in the usual form. 



132 METHODS OP TEACHIXO. 

The sounds of the letters ma^^ also be indicated by using 
the diacritical marks of the dictionar3% This method has 
been used by many teachers with great success. It has been 
very thoroughly tested. in the schools of Columbus and else- 
where. If the primer or primary reader used in the school 
has no marks, the teacher can mark the words neatly with pen 
or pencil. The method of Dr. Leigh has also been tested in 
several of the principal cities of the country, and is regarded 
by leading educators as the most practical yet presented. 

In favor of the Phonic Method, we remark that it is natural, 
philosophical, and practical. It is not a mere theory ; it is a 
method of great practical value. It is not an untried experi- 
ment ; its utility has been demonstrated by the test of our 
best teachers. No intelligent teacher who adopts it will ever 
discontinue its use ; and it is difficult to see how a teacher can 
be intelligent who has not adopted it. The indications are 
that it will soon be universally adopted in this country. 

Other 3Tethods- — There are several other methods that 
have been used in teaching pronunciation, the most prominent 
of which are the Alphabetic and Phonetic Methods. Besides 
these there are several modifications of the Phonic Method, in 
which special forms of letters are suggested, which may be 
included under the general name. Typographic Method. 

Alphabetic Method. — The Alphabetic Method is that in 
which the teacher attempts to teach pronunciation by having 
the pupils call the names of the letters. Thus in the word 
fight, the teacher has the pupil say ef, eye, ge, aitch, tee, and 
then pronounce the word fight. The thought was, if there 
was any thought on the part of the teacher, that the naming 
of the letters of a word would enable the pupil to pronounce 
the word. 

This method was formerl}^ the only one used in our schools. 
Nearly every adult of the pi'esent day was taught to pro- 
nounce words in this way. The method, however, is an ab- 
surdity. No one ever actually learned to pronounce words in 



TEACHING PRONUNCIATION. 133 

this way, though teachei-s have attempted to teach in this 
yfuj. Children who were required to learn in this way, act- 
ually learned by association and the phonic principle. They 
heard the teacher pronounce the words several times, and 
remembered the pronunciation, associating the name of the 
word with its form. They also unconsciously acquired a 
knowledge of the powers of the letters, so that when they saw 
them or named them in words, they knew what their powers 
were. They were often guided also by analogy in pronounc- 
ing similar words. 

The objection to the method is that the name of the letter 
is not its sound. In many cases, the name not only does not 
suggest the sovind, btit beai's no relation to it. How, for in- 
stance, can any learner know that the sounds represented by 
aitcli^ eye, double ell, spell the word hill. If we should pro- 
nounce words by uniting the names of their letters we should 
have quite a different word from the one intended. Thus me 
would spell the word evi-me, at would spell eigh-ty, leg would 
spell el-e-gy, ntt would spell en-H-ty, iitk would spell ti-ti-ca, 
etc., and what the names of the letters of such words as 
brought and phthisic would spell, we leave to the ingenuity of 
the teacher who still uses this method, A method so evi- 
dentl}^ absurd should no longer find a place ir> our schools. 

Rev. Thomas Hill, one of the most eminent educators of 
the age, says: " In teaching a child A, B, C, and impressing 
on his mind that these letters spell the words of the language, 
you teach him a falsehood and give him little chance to detect 
the cheat. I say, so far from helping him to read, j'ou have 
put a formidable obstacle in the wa^' of his learning to read. 
The letters do not spell the words, and therefore the knowl- 
edge of the letters does not aid him in reading the words ; 
they do spell something else, and therefore are an actual 
hindrance in learning to read." 

Dr. Currie apologizes for those who use it, saying that " it 
is not designed to be a reading method alone ; but a method 



134 METHODS OF TEACHING. 

for teaching reading and spelling simultaneouslj^, and the 
reading through the spelling." He also sa^'s, "It does not 
pretend to be a phonic method," etc. " Very much of the 
argument against the common method has proceeded on the 
false assumption that the \ettev-7iames of a word and its sound 
are set forth in the relation of phonic parts to their whole ; 
and has therefore not touched the merits of the question." It 
is clear, however, that most teachers who used this method did 
so to teach their pupils to pi'onounce words, for it was a 
common thing, when a child came to a word in his reading 
lesson which he could not pronounce, for the teacher to tell 
him to " spell the word." 

Phonetic 3Ietho(l. — Another method, formerly used to 
some extent, is that which has been called the Phonetic Method. 
This method is the same in principle as the Phonic Method; it 
differs from it in introducing about fourteen new characters 
instead of using a notation ; and also in using onlj^ the 
letters in spelling a word, which are sounded in it. 

In teaching by this method, the elementary sounds were 
taught, then the twenty-six letters as representatives of twen- 
ty-six of these sounds, and then about fourteen new charac- 
ters to represent the remaining words. Then pupils were 
taught to combine these characters into words, using only as 
mau}^ characters in spelling a word as there are elementary 
sounds in it. Thus, the word light would be printed lit; hear, 
bar, etc. These words could of course be readil}^ pronounced 
by the pupil. 

Pupils were then required to make the transition from 
words in their phonetic forms to the common forms. This 
was done by having words in the two forms printed in parallel 
columns, so that the comparison could be readily made. The 
word in the phonetic form was thus a sort of key to the pro- 
nunciation of the word in its ordiuary form. This method, 
though once popular with a certain class of teachers, is now 
obsolete. 



TEACHING PRONUNCIATION. 135 

III. Correct Pronunciation. 

Haviug shown how a child may be taught to pronounce 
words, we pass on to consider the art of correct and artistic 
pronunciation. Correct pronunciation includes two things; 
Articulation and Accent. Every mistake made in the pro- 
nunciation of a word is an error of either articulation or 
accent. 

Articulation. — The basis of Pronunciation is Articula- 
tion. The voice must be moulded into the elementary 
sounds of the language, as a primary condition of expressing 
words. This moulding of the voice is called Articulation. 
Articulation is the special characteristic of human speech and 
of mankind. Man is the only animal that can make and com- 
bine articulate sounds. 

Nature of Akticulation, — Articulation is the correct 
and distinct utterance of the elementary sounds of the lan- 
guage. The term is derived from articulus, a joint, an ar- 
ticulate sound being literally a jointed sound. Articulation 
difters from Pronunciation as a part from the whole ; for while 
the latter refers to the utterance of the entire word, the for- 
mer has reference to the utterance of the elementary parts of 
a word. The term Enunciation, from e, out of, and nuncio^ I 
announce, is used by some writers as synonymous with Articu- 
lation, and by others as meaning the utterance of the element- 
ary sounds as' combined in words. 

There are about forty elementary sounds in the English lan- 
guage, though orthoepists are not agreed with respect to the 
exact number. Some vowel sounds, which are regarded as 
simple by one writer, are shown by other writers to be a com- 
bination of two simple vocals. Webster and Worcester give 
about forty distinct sounds, and this is sufliciently correct 
for all practical purposes. 

These elementary sounds are made by the organs of the 
mouth and throat, called the Organs of Speech. The organs 



136 METHODS OF TEACHIXQ, 

of speech ma}^ be regarded as a set of flexible moulds which 
give form to the voice which flows into and through them. 
Amy imperfection in the moulds or their arrangement will tend 
to impair the articulation. In order to articulate correctly, a 
pei'son must possess a complete control over these organs, so 
as to be able to mould the voice that comes up from the larynx 
into all the possible forms required. 

In the standard dictionaries all the sounds of the language 
are presented, and the diacritical marks which indicate them. 
The slight shades of difference between the sounds of some 
of the vowels, when occupying different places, and their 
modifications by being associated with other letters, are also 
explained. All of this knowledge is of great importance to 
teachers, and should be thoroughly mastered by them. 

The importance of correct £^^■ticulation is very great. It is 
the basis of accurate and finished utterance. A correct and 
artistic articulation will sometimes atone for a bad voice. 
The secret of the power of Randolph's oratory, it is said, lay 
in his articulation, for his voice was creaking and disagreea- 
ble, but by culture it " became so fascinating" that it 
"haunted the hearer like the spell of an enchantress." 

Artistic articulation is capable of producing deep and vivid 
impressions on the listener. A speaker in uttering the ex- 
pression "the hiss of a serpent," by slightly prolonging the 
final sound of hiss so touched the imagination of one of his 
hearers that it led to a vivid dream of a serpent. Prof. 
Thwing mentions a speaker who just before his departure for 
the Pacific coast, in an address spoke of "the wash of its 
waves," and by giving a slight fullness to sh, made an impres- 
sion on his mind that he says he has never forgotten. 

Methods of Teaching. — Correct Articulation is taught in 
three ways: by Imitation^ by Phonic Analysis, and b}' Cor- 
recting the Errors of pupils. 

TitiUaUori. — The pupil learns Articulation principally by 
imitation. The child will naturally speak like his parents and 



TEACHING PRONUNCIATION. 137 

companions. If their enunciation is pure and correct, bis will 
be pure and correct also; if theirs is incorrect, his will also 
be incorrect. Pupils will also imitate their teacher; he should 
therefore be exceedingly careful that he presents a model of 
correct and elegant enunciation. 

Phonic Anali/sis. — Pupils should also have daily drill on 
the elementary sounds. The ear thus acquires a correctness 
and delicacy of perception, and the organs are trained to give 
accurately, promptly, and with ease, all the sounds of the lan- 
guage. Especial drill should be given upon the more difficult 
sounds and those we are most liable to get wrong. Words 
should be given for the pupils to analyze into their elementar}- 
sounds. Such a drill has been called Phonic Analysis. 

Phonic Analysis should receive the careful attention of the 
teacher. It is the foundation of all distinct articulation and 
correct pi'onunciation. Many of the faults of pronunciation, 
so frequently met with, may be prevented or removed by per- 
sistent drilling on the elementary sounds. Phonic Ana,l3^sis 
should include an exercise on the vocals, subvocals, and aspi- 
rates, by themselves and in combination. Great variety can 
be given to the exercises, and a very great degree of interest 
aroused in the subject. Phonic analysis should not be re- 
stricted to the lower grades, but should constitute a pai't of 
the instruction in reading or elocution in every stage. The 
vocal organs need constant technical exercise, like the fingers 
of a pianist or violinist, that they may perform their offices 
with ease, accuracy, and ai'tistic excellence. 

Care should be taken to correct the errors of omission, as 
well as those of commission. We often suppress sounds as 
well as make incorrect ones. The ear should be trained to 
distinguish all the finer shades of difference in sounds ; and the 
organs of speech should be carefully trained until they are able 
to produce promptly and with ease all the sounds of the lan- 
guage, in all their varied and complex combinations. And 
this can best be attained by the exercises in Phonic Analysis. 



138 METHODS OF TEACHING. 

Words and sentences containing difficult combinations 
should be repeated. Take such words as strength^ shrubs, 
stretched, etc. Practice also uttering difficult sentences, such 
as "She sells sea-shells," "I saw six slim saplings," "There 
were three gray geese and three graj^ ganders," " Around the 
rugged rock, the ragged rascal ran." Pupils may be required 
to repeat the well known combinations, " Peter Piper" " The- 
ophilus Thistle," " Amidst the mists," etc. A drill of a few 
minutes each daj^ on sucli exercises will be found to be of great 
value to pupils. The words should be repeated as rapidly as 
they can be spoken with distinctness. Such a drill can be 
given to each reading class, or the entire school may have 
an exercise for two or three minutes once or twice a day. 

Errors of Articulation. — There are several special defects 
in articulation, the most prominent of which are Stammering, 
Lisping, and Bad Habits. 

Stammering. — Stammering is a hindered or obstructed 
utterance of words. It is due to various causes, which should 
be understood, in order to overcome it. Sometimes it is the 
result of some peculiarity of the vocal organs, and can be 
cured by speaking with a marble or pebble in the mouth. 
Demosthenes is said to have overcome a defect in enunciation 
by declaiming with pebbles in his mouth. 

Sometimes stammering is merelj'- a habit acquired by asso- 
ciating with companions who stammer. Sometimes it is the 
result of rapid and heedless talking. Sometimes it is the 
result of an exuberance of feeling, as persons often stammer 
when excited or angry. In these cases, care on the part of 
the pupil to speak slowly and with deliberation, will be suffi- 
cient to overcome the habit. Sometimes stammering is due 
to timidity on the part of a nervous or sensitive pupil, in 
which case the teacher should endeavor to give him confi- 
dence in himself, and make him feel at ease. 

More frequently, stammering arises from some peculiarity 
of the nervous system, either natural or the result of disease. 



TEACHING PROXUNCIATIOX. 139 

The great remedy in such cases is speaking slowly. We have 
known persons to be cured by practicing talking "to time," 
beating time with the finger and speaking their words at 
measured intervals. The nervous s^^stem seems to respond 
to the rhythmical movement, as is s'een in the fact that per- 
sons who stammer when they talk or read, will not stammer 
in singing. For the same reason it will be found that pupils 
who stammer read poetry more easily than prose. Another 
suggestion is that the pupil accustom himself to a clear idea 
of what he is to say before he begins to speak. Deliberation 
and confidence are essential elements of a cure in nearly every 
case. An intelligent common school teacher can usually cure 
the most inveterate cases of stammering, if he will persevere 
in the attempt, and is able to secure the assistance of the pupil. 

Limping. — Lisping is mainly the use of the sound ///, for s. 
It is a habit found more frequentl}^ among girls, as stammer- 
ing is more frequent among boys. Sometimes it is a mere 
affectation of speaking, in which case it can be cured by show- 
ing the pupil how it mars the speech, and perhaps by using a 
little judicious ridicule. 

More frequently, lisping is a natural defect of enunciation, 
caused by some peculiarity of the organs of speech. Occa- 
sionally it is due to the tongue being a little large, or a little 
too long. A person will sometimes lisp, also, when the front 
teeth are very lai'ge or ver}^ prominent. To correct the habit, 
in these cases, tlie pupil must first be led to notice the defect 
in liis articulation; a person sometimes lisps and is not aware 
of it. The pupil must then be shown the positions of the 
organs in making the sound of s, and the sound of th^ and be 
carefully drilled on these two sounds, and then on words con- 
taining the sound of s, until they can be correctly pronounced. 
It often requires persistent practice to overcome the defect, 
but it should be continued until cured. 

Bad Habits. — Pupils often acquire the habit of incorrect 
or imperfect articulation by carelessness in talking, or by the 



140 METHODS OF TEACH I XG 

imitation of incorrect forms of speech common in their neigh- 
borhood. Such words as lohich, where, token, etc., are vevy 
generally mispronounced by omitting the sound of h, which, 
though written after the w.'„is sounded before it. The words 
shrub and shrink, pronounced srub and srink^ illustrate the 
same error. Final ing is often abbreviated to in; as nothing, 
something, etc., called nothin, somethin, etc. There are hun- 
dreds of such errors, which teachers should notice and try to 
correct. 

Some of the most common errors of articulation found in the 
public schools of several States are those which arise from the 
early use of the German language. We call attention to some 
of the most prominent of these errors. Pupils confound the s 
and z, calling is, iss instead ofiz; his, hiss instead of hiz, etc. 
They confound v and w, saying wine for vine, and vine for 
ivine, etc. They confound s and th, saying ivis for with, sin 
for thin, thick for sick, etc. They confound ch and^, asjurch 
for church, chug for jug, Chon for John, etc. They confound 
d and t, as " town the hill" for "down the hill," and "I can't 
to it" for "I can't do it;" they confound d and th, a,s den for 
then, and even b and jj as braij for pray, prick for brick. 

In New England there is a peculiarity of pronunciation 
which consists in adding the sound of r to the end of words 
ending with the Italian sound of a, as idear, arear, etc. At 
the same time, there is a tendency to omit the sound of r at 
the end of words ; as, watah for water, daughtah for daughter; 
and to omit or soften the r in other places ; as N'ew Yawk for 
New York, etc. This peculiarity reminds one of the English- 
man's trouble with his 7)-'s, his tendency being to use the h 
where it does not belong, and to omit it where it does belong, 
saying ^oase for house and hobject for object. Many other 
States, though not presenting so striking a peculiarity as 
the New Englander's r, have much more serious defects in the 
articulation of their people. 

To overcome these bad habits, two things are required. 



TEACHIXG PRONUNCIATIOxV. 141 

First, tlie pupil must be led to perceive that he makes the 
mistake ; the ear must be trained to detect the difference of 
the sounds, and to notice when the incorrect one is given. 
Second, the pupil must be taught the position of the organs 
in making the sounds, and be drilled upon them until he can 
make them at his will. Then it will require constant atten- 
tion on the part of both teacher and pupil in order to break 
away from the old habit and acquire the new one. 

Besides these special errors, there is a class of general ones 
that demand notice. The word and is badly abused in pro- 
nunciation, often being passed by " with merely an uncourteous 
nasal salute." The terminations ness and le^s are often 
changed to niss and /i's.s, ment to munt, and ow into er, as 
feller for fellow^ piller for pillow, etc. Words are man'ed also 
by the omission of sounds ; as histry for history, evry for 
every, reglar for regular, Fehuary for February, etc. 

Accent. — The second condition for correct pronunciation 
is Accent. When the elementary sounds are made correctl}', 
and the stress of voice falls on the proper S3'llable, the word 
is pronounced correctly. We shall speak of the Nature of 
Accent, and Methods of Teaching it. 

Nature of Accent. — Accent is a stress of voice upon one 
or more syllables of a word. The term is derived from the 
Latin, ad, to, and cantus, a song, showing that accent was 
primarily related to singing. 

Accent gives a musical element to speech, and adds to the 
beauty and harmony of language. The ancient languages dis- 
tinguished syllables by what is called quantity ; that is, as 
long and short syllables. The French language is so nearly 
deficient in accent that blank verse is an impossibility in 
French literature. 

Accent is of two kinds. Primary and Secondary. Primary 
Accent is the stronger accent in pronouncing words; Second- 
ary Accent is the weaker or slighter accent in pronouncing 
words. In some words the secondary accent is almost as 



142 METHODS OF TEACHING. 

strong as tlie primaiy; as, vioJiit, caravan^ orlisan, etc. 
Some words have two secoiidaiy accents ; as, incomprehensi- 
hility and antipestUeiitial. The word amen has both syllables 
accented ; and man_y compound words have a slight secondary 
accent, as gai)i-say, light-house, etc. 

The primary and secondai-y accents are, in many cases, so 
nearly equal that they are frequently exchanged, the primary 
becoming secondary, and the secondary primary. Many 
words, such as ar'tizan, rev'erie, in' valid, etc., have trans- 
ferred the primary accent from the last to the first syllable. 

All words in the English language of more than one sylla- 
ble have one accented syllable ; and most polysyllabic words 
have a primary and a secondary accent. It is a general ten- 
dency of the language to place the accent on the first syllable 
of dissyllables, and on the antepenult of polysyllables. The 
exceptions, however, are so numerous, that this is not to be 
regarded as a rule, but only as a general tendency of pronun- 
ciation. With respect to verbs of two syllables, the tendency 
is to place the accent on the second syllable. 

Principles of Accent. — Webster's Dictionary lays down 
several principles which seem to have been operative in deter- 
mining the position of the accent of words, and also in chang- 
ing it from a former or retaining it in its present place. 

First. Derivative words take for a time, if not permanently, 
the accent of the original words from which they are formed. 
The same rule holds good with words derived from other 
English words b^' adding one or more s^yllables to their begin- 
ning or end ; as, improp'er from prop'er, pleas'antly from 
pleas'ant, etc. 

Second. Ease of utterance has some influence in deciding 
the place of accent. Thus, accept'ahle was formerly pro- 
nounced ac'ceplable, lUen'sil Avas u'tensil, dyspep'sy was dys'- 
pepsy, suhal'tern was sub'altei'n, etc. This principle is an 
important one in determining the place of accent, and though 
many will cling to the older and harder pronunciation as 



TEACHING FROiXUNCIATION. 143 

marked in the dictionaries, the changes which promote ease 
of utterance will finally prevail. 

Third. In words of two syllables there is a tendency to 
accent the first or penultimate syllable ; as, com'mon, proij'er^ 
dis'cord, etc. This principle, however, has many exceptions. 
It meets with a powerful counteraction from the first princi- 
ple, it being natural in derivative words to place the accent on 
the radical part of the word ; as, confer' , didend', amuse', etc. 
There is a constant struggle among the common people, how- 
ever, to draw back the accent to the first syllable; and thej'^ 
being in the majorit}^, are slowly gaining on those who are gov- 
erned by the first principle. 

Fourth. In words of three or more syllables, there is a 
strong tendency to accent the antepenult, or third syllable 
from the end; as in el'oquent, ac'cidenf, opjiortu'nity, etc. 
This tendency is also counteracted by that of derivation, 
which tends to arra}^ scholars against the mass of the people, 
many scholars saying contem'plate, demon' d rate, etc., while 
popular usage is con' template, d evi' on str ate, etc. 

There are several other principles which influence the place 
of the accent. Thus, we accent a word of two syllables when 
used as a noun or an adjective on the first part ; and when 
used as a verb, on the second part ; as con'vert and convert' ^ 
jji'o'test and p7'otest', etc. For a fuller discussion of this sub- 
ject, see Webster's Dictionary, from which these facts and 
principles are drawn. 

Method of Teaching. — We teach the correct accent of 
words by Imitation and Correcting Errors. 

Iinitatloii. — The teacher should be careful to place the 
accent correctly in speaking his words, that his pupils may 
have correct models for imitation. If the teacher continually 
sa3'S i'dea and in'quiry, his pupils will naturally make the 
same mistakes. Every teacher should make it a special aim 
to pronounce his words correctly. He should make the dic- 
tionary a constant study, and also lead his pupils to acquire 



144 METHODS OF TEACHING. 

the "habit of consulting the dictionaiy to find out the correct 
pronunciation of words. 

Errors of Accent. — One of the most common errors in the 
pronunciation of words, is that of misplacing the accent. 
Comparatively few persons, for example, pronounce idea with 
the accent on the second syllable, or complex and construe 
with the accent upon the first syllable. 

There is a strong tendency in this country, among the 
common people, to give a marked secondary accent on certain 
words, which properly have but one accent; as, difficulty, 
cir'cumstan'ces, in'terest'ing, etc. Another custom, even 
more vulgar, consists in placing, in words having an unac- 
cented initial S3dlable followed by an accented one, a nearly 
equal stress of voice on both ; as in ex'act'ly, gi'gan'tic, 
i'tal'ic, po'lit'ical, etc. Dickens, ridiculing it in Martin 
Ghuzzlewit, makes one of his characters say, " Perhaps there 
ain't no such lo'ca'tion in the ter'rito'ry of the great U'ni'ted 
States." The English, however, often go to the opposite 
extreme, and slur over the unaccented syllables so as to rob 
them of the true force which belongs to them. 

The attention of pupils should be called to such mistakes, 
and pains should be taken to have them corrected. Pupils 
should be required to keep a list of the words which the}" mis- 
pronounce, and should be exercised on it frequently to see 
that they are correcting their mistakes. It requii*es constant 
care and much practice to change from an incorrect to the 
correct pronunciation of a word. 

Teachers should also make out such a list and drill them- 
selves daily on all words which they find they have been mis- 
pronouncing. Many of them will be surprised at the extent 
of the list, and at the difficulty of the task of correcting their 
errors. It will sometimes take months and even years to cor- 
rect some old habit which has become fixed by years of incor- 
rect practice. 

The following is a brief list of quite common words which 



TEACHIXG PKONU-N'CIATION. 



145 



are frequently mispronounced. Let the pupil and young 
teacher examine this list and correct any of their mispronun- 
ciations, and use it as the nucleus of other words which they 
find they have been mispronouncing : 



ere, 


often. 


ai-ea. 


inquiry, 


Asia, 


ne'er, 


soften, 


vicar, 


vagary, 


Sinai, 


food, 


extol. 


visor. 


equation. 


Alpheus, 


root, 


route, 


gratis. 


museum. 


gopher. 


dost. 


again. 


complex. 


lyceum. 


Arabic, 


doth, 


recess. 


compound. 


interesting, 


Philippi, 


bade. 


depot. 


construe, 


illustrate. 


Phenice, 


truths, 


carry, 


extant, 


contrary, 


Delilah, 


shew, 


leisure, 


gallows, • 


opponent, 


Gennesaret, 


iron, 


exhaust. 


cortege, 


disputant. 


Caucasian, 


idea, 


apostle. 


abdomen, 


vehement. 


Ai'istobulus, 


error, 


epistle, 


courtesy. 


nominative. 


Sardanapalus. 



Recitations, now and then, say as often as once a week, in 
the pronunciation of words, will be of great benefit to pupils. 
There is no reason why we should not have " Pronunciation 
Matches," as well as " Spelling Matches," in our schools; and 
the teacher who introduces them will find them of great value. 

JProiioiinring Match. — In a Pronouncing Match, the 
teacher will spell the words orally or write them upon the 
blackboard, and assign them to the pupils in regular order, as 
in the spelling match, the pupils "trapping" or "going out," 
as may be preferred. The following rnethod is suggested by 
Mr. Woodruff : — Make out three lists of words, and mark them 
A, B, and C Give the list marked A to the class, and when 
all are " pronounced out" but one, betakes his seat as entitled 
to a premium. Call the remainder up again and do the same 
with list B, and then again with list C, thus selecting two 
others entitled to a premium. Then call up these three 
" premium pronouncers," and assign them words, the last 
down receiving the first prize, the second down the second 
prize, etc. 
7 ' 



CHAPTER V. 

TEACHING ORTHOGRAPHY. 

ORTHOGRAPHY is the art of expressing the elements of 
words. These elements may be expressed either orally or 
in writing. When expressed oralty, the names of the charac- 
ters may be given, or the sounds which they represent ; the 
former is the common oral spelling ; the latter is called pho- 
netic spelling. Words may also be spelled either upon hear- 
ing them pronounced, or upon merely conceiving them. 

The term Orthography is from orthos, right, and grapho, I 
write, meaning literally, to write right. In its primary 
meaning it thus refers to written spelling, and this was its 
original use. Oral spelling is a secondary and derivative idea 
and practice. In its true sense, orthography is the represent- 
ation of spoken language by visible signs. It had its origin 
in picture-writing, and has gradually passed down through 
the verbal and syllabic stages to the alphabetic S3'stem, our 
present letters being abbreviations and modifications of pic- 
tures. 

I. The Nature of Orthography. 

Importance. — The importance of orthography has been* 
sometimes over-estimated and sometimes under-estimated. 
Some teachers have made it a hobby in the schools, and others 
have treated it with neglect and even with contempt. Its true 
value may be stated in a single sentence : there is no great 
credit in. being a good spoiler, but there is great discredit in 
being a poor one. Dr. Currie gives a similar estimate when 
he says, " The possession procures no credit, but the want 
entails disgrace." Prof. March saj^s, " Stress is laid on it as 

(146) 



NATURE OF ORTHOGRAPHY. 147 

the sign of a thoroughly educated person out of all proportion 
to its real value." Still, correct spelling can not but be 
regarded as an indication of a cultivated and scholarly mind. 

The attention it has received during the past fifty years has 
varied. Many years ago, when there were few studies in 
the public schools, orthography occupied a large share of the 
teacher's attention. The old " spelling schools" have become 
historic. Subsequently, when geography, grammar, mental 
arithmetic, etc., were introduced, orthography was eclipsed in 
interest, and was greatly neglected. After a while, it was seen 
that boys and girls were coming out of the pviblic schools 
poorer spellers than their parents, and a reaction took place 
in favor of orthography. To-day it is receiving its just share 
of attention. 

Difficulty. — .English orthography is exceedingly difficult : 
it is probably more difficult than that of any other modern 
language. American children spend three years in learning 
to spell a little, while German children get further in a 
twelvemonth. In the civil examinations in England, out of 
19T2 failures, 186G candidates failed in spelling; and it is said 
that the documents prepared by the prime ministers of Eng- 
land show that no one of them could have passed these exami- 
nations in spelling. 

This difficulty is due to the irregularity of the English 
orthography. This irregularity consists in the use of silent 
letters, and in the use of different letters and combinations to 
represent the same sound. Many letters are pronounced in 
several different ways, while the letters or combinations of 
letters for a single sound, in some cases amount to scores. 
Many words of no more than two syllables may be spelled in 
several thousand different ways, by the use of combinations 
actuall}^ employed in other words in the language. The word 
scissors, it is computed by Ellis, may be thus written in 
nearlj^ 6000 different ways. Indeed, it may be truly said that 
we possess the worst alphabetic spelling in the world. Eug- 



14:3 METHODS OF TEACHING. 

lish orthography- is "the opprobrium of English scholarship;" 
it is the greatest hindrance to education and to the spread of 
our language. 

Origin. — The irregularity of our orthography is accounted 
for by its history. The Anglo-Saxon was first reduced to 
writing b}' the Roman missionaries who converted the people 
to Christianity. They used the Roman letters, in nearly their 
Roman value, and added new characters for the sound of a in 
fat^ th in their (dh), th in thine, and lo. The Norman Con- 
quest produced chaos in English spelling. The Normans and 
Saxons could not pronounce each other's words correctl}'. 
The scholars inclined to spell in the old book-fashion ; but the 
Normans dropped the special Anglo-Saxon discrimination, 
and left in words many of their own letters which were not 
pronounced by the people ; and many letters were inserted to 
no purpose in ill-directed attempts to represent the strange 
combinations. 

A change in the vowel sounds then followed. The close 
vowels changed, under the accent, into diphthongs, by taking 
an a sound before them. The old t, as in machine, has thus 
changed to ai, as in mine ; u as in rule has given rise to au, 
as in house. The open and mixed vowels have become closer ; 
a, as in far, changing to a (i. e., e) m fate or wall, or to o in 
home (A-S. ham); e as in they, changing to e (i. e., i) in me ; 
as in foe, changing to oo (i. e., u) as in moon (A-S.,Wi6«o). 
Single characters have thus come to stand for diphthongs, and 
the long and short sounds, which go in pairs in other lan- 
guages, are denoted in ours by different characters, and come 
from diflFerent sources. Intermediate between the old a (far) 
and e {met), has become established a in fat, fare ; between a 
(far) and o (note), o in not and nor, and the sounds of u in 
hut, burn, have also arisen. All these have no special signs ; 
and four consonants, sh, zh, th, dh are in the same condition. 

Carelessness in authors and copyists also contributed to 
tiiis irregularity. Before the time of printing, manuscripts 



TEACHING ORTHOGRAPHY. 149 

show that the widest license prevailed in spelling words. 
Even proper names are found recorded in a great multitude 
of forms, several variations being sometimes found in the 
same manuscript. Disraeli says that " Leicester has sub- 
scribed his own name eight different ways," and that "the 
name Villers is spelled fourteen different waj^s in the deeds 
of that family." Lower states that the family of MainwaiHng 
has 131 A^ariations of that single name, all drawn from author- 
ized documents. 

There were a few writers, however, in those early days, who 
were attentive to the proper- form of words. The spelling of 
the Ormulum, which was written in the 13th centmy, though 
strange and cumbrous, is remarkable for its regularity; and 
the author urges his copyists to follow his orthography with 
the utmost exactness. Chaucer, also, more than a century 
later, carefully revised and- corrected his own works ; and he 
enjoined upon his scribe to "write more trew" that which 
was intrusted to him, saying that he was obliged " it to cor- 
rect and eke to rubbe and scrape," because of the negligence 
and haste with which it had been copied. 'Even as late as the 
time of Shakespeare, orthography was very unsettled, for the 
name of the great poet was w^ritten more than thirt}^ different 
ways. 

The invention of printing contributed largely to fix the 
orthography of words. For a long time, however, it did but 
little to give uniformity' to spelling. There being no standard, 
printers added or omitted letters, as the length of the line or 
convenience of spacing required. The same word was often 
printed in several different ways on the same page. At length 
the attention of scholars was directed to the subject, and 
efforts were made to improve and settle English orthography; 
but not much was accomplished until the time of Dr. Johnson. 

Dr. Johnson's celebrated Dictionary, published in 1155, was 
the first recognized standard, of orthography; and it has con- 
tributed more than any work, either before or since, to fix our 



150 METHODS OF TEACHIXG. 

method of spelling. It settled usage definitely in favor of 
some one of the numerous forms in which Avords were written, 
and thus removed the cause of confusion. He introduced 
changes to restore the ancient orthography or to remove some 
anomaly, some of which were not adopted by subsequent 
writers. Among these were the restoration of k to mau}^ 
words that had been written without it ; as, musick^ rhetorick, 
etc., and the insertion of u in many words ending with or, as 
honour, ancestour, etc. This latter method is still used by 
many English writers. 

In 1828, Noah Webster published his great Dictionary of 
the English language, in which he made many changes in 
orthography. These changes were of two kinds: first, to 
make the words correspond, as far as practicable, with their 
primitive forms, so as to reveal their etymological affinities ; 
second, to reduce as much as possible the number of anomalies 
and special cases. Of the former class, many were restored 
by Dr. Webster in the second edition of his work, published 
in 1840; and others were restored in subsequent editions. 
Many alterations of the second class have been received with 
favor and adopted by a large number of writers in the United 
States, and by some English authors. 

Phonetic Systems. — The irregularity of English orthogra- 
phy has led to many attempts for the adoption of a phonetic sys- 
tem of spelling. The first of these was made by- Sir Thomas 
Smith (15G8), Secretary of State to Queen Elizabeth. He 
was followed by John Hart (1569), Chester herald, by William 
Bullokar (1580), by Dr. William Gill (1619) Master of St. 
Paul's School, London, and in 1633 by Charles Butler, who 
printed a book in which his new method was employed. In 
the time of Charles I., many changes were introduced, and it 
was very common, even among eminent scholars, to spell 
words as they were pronounced, omitting such letters as were 
deemed superfluous. These attempts, however, being made 
upon no settled or uniform principles, had little or no perma- 
nent effect upon the language. 



TEACHING ORTHOGEAPIIY, 151 

The attempt to reform our orthography by employing an 
alphabet in which each sign shall stand for one and only one 
sound, has been made in modern times. Dr. Franklin in- 
vented such a system, though he never brought it to perfec- 
tion, and scarcely used it except in a brief correspondence with 
a friend. The most important systems recently presented 
are those of A. J. Ellis, I. Pittman, E. Jones, and A. M. 
Bell. Mr. Bell has invented a set of characters which indicate 
by their form the positi(m of the organs of speech, being thus 
a system of " visible speech." Scholars have begun to use it 
in scientific treatises; but it can hardly meet with general 
adoption. Mr. Pittman's alphabet contains 16 new letters, 
and several books are printed in this system. The systems 
of Mr. Ellis and Mr. Jones are based on the present spelling, 
using always the same letters for each sound, selecting that 
sound which it oftenest represents. The advantage of this 
system is that it can be set up with the common printer's 
type, and can be read by those who can read the present 
spelling. Its defects are that letters have different values in 
combination from what they have alone, and that so many 
elementary sounds are represented by digraphs. In this 
country various systems of spelling have been advocated, but 
none has yet been devised which secures general approval. 

. JReforminSiyelUnfj. — There seems to be a growing opinion 
in favor of a reform in our orthograph}'. The leading philol- 
ogists of this country and England are becoming strong 
advocates of it. Among these we may mention the names of 
March, Whitney, and Haldeman, of America, and Max Miiller, 
Ellis, Jones, etc., of England. Many of the philological and 
teachers' associations of both countries, and also some state 
legislatures, have appointed committees to consider the subject. 

The disadvantages of our present system make a change a 
necessit3\ Our system of spelling is one of the greatest hin- 
drances to the education of our people. Children require 
years of study in oi'der to learn to spell and pronounce written 



152 THETIIODS OF TEACHING. 

words, which could be learned, if we had a phonetic system, 
in a few weeks or months. Besides this, millions of dollars 
are wasted eA'erj' 3'^ear in printing silent letters and senseless 
combinations to express simple sounds. 

That some change will be made, seems probable, but what 
form it will assume, it is difficult to tell. The essential prin- 
ciple of a radical change is that each sound shall be repre- 
sented by a single character, and that words shall be spelled 
as pronounced. We should therefore take the present letters, 
using each for its most common sound, invent some fourteen 
or sixteen new characters for the remaining sounds, and then 
spell words as they are pronounced, using no more characters 
in a word than are sounded. 

The objections to this, however, are many and serious. 
What shall be done with the vast libraries of books already 
printed, which will become sealed volumes to those taught by 
the new method ? How shall we get the people to learn the 
new method, or to allow it to be introduced into the schools 
of the country? Indeed, the objections are so great as to be 
absolutely insuperable. It may therefore be positively as- 
sumed that no phonetic system will be adopted ; and in what 
form a reformation will come it is at present impossible to 
pi'edict. 

TI. Methods of Teaching Orthography. 

There are two methods of teaching orthography, which may 
be distinguished as the Oral and the WiHtten Method. The 
Oral Method depends upon the sense of hearing, and the 
Written Method upon the sense of sight. They have also 
been distinguished as the Auricular {auris, the ear) and the 
Ocular (ocultis^ the e3^e); but the terms Oral and Written 
seem to have been more generally adopted by the profession. 

The Oral 3Iefhod The Oral Method is that which 

teaches orthography by naming the letters of words ; it is 
based upon the principle of fixing in the memory the letters 



TEACliiXG ORid JGRAFIir, 153 

of wordr!i in their order through the sense of hearing. It con- 
sists in memorizing the sound-order of letters, witli the 
expectation that the association of the names will become 
iixed in the memory in their proper order lilvc the words of a 
quotation. 

The Oral Method possesses several advantages. It teaches 
pupils to pronounce words, which the Written Method does 
not. It also teaches the correct syllabication of words, which 
is not done b}^ the ordinary Written Method. It also admits 
of several interesting methods of competitive recitation. The 
spelling-match is essentially an oral exercise : a written spell- 
ing-match is a dull thing, compared with the old-fashioned 
oral spelling-matches. 

There are also several disadvantages in the Oral Method as 
compared with the Written Method. First, pupils taught to 
spell orally will not usually spell correctly when they are 
writing. It is frequently noticed that piipils will spell without 
mistake, when pronounced to them, the words which they 
have misspelled in a letter or a composition. This objec- 
tion becomes more serious when we remember that the princi- 
pal value of spelling is the ability to write words correctly. 
There is no particular value in spelling words orally. An- 
other objection is that each pupil of a class cannot spell as 
many words of the lesson as by the Written Method. 

The Oral Method, notwithstanding these objections, is the 
one which has been almost exclusivel}^ used for centuries. It 
is within a comparatively recent period that the Written 
Method has been introduced into our schools. Our fathers 
were all taught by the Oral Method, and even the majority of 
the teachers of the present day w^ere trained bj^ it. 

The Written Method 'The Written Method is that which 

teaches orthography by writing the letters of words. It is 
based upon the principle of fixing the orthographical struc- 
ture of words upon the memory through the sense of sight. 
It assumes that the word is presented to the mind as a pic- 



154 METHODS OF TEACHING. 

ture, in which the elements are distinct!}' perceived and 
remembered in their order. - 

There are man}'^ advantages of the Written Method as com- 
pared -witli the Oral Method. First, we learn to spell more 
readily hj sight than b}' sound. That which we see makes a 
deeper impression on the mind than that which we hear. The 
old adage that "Seeing is believing," expresses this fact. In 
proof of this principle, it is said that the deaf, who must use 
the Written Method, learn to spell more readil}' than the 
blind. It is also a common exi^erience, that when, in writing 
a letter, we are in doubt about the orthography of a word, we 
write it on a piece of paper to see how it looks. Good spell- 
ers tell us that in spelling orally they usualh^ picture words 
in their minds, and name the letters accordingly. 

A second advantage of the Written Method is, that a pupil 
taught b}' this method will spell correctly when he writes, 
which is the principal point aimed at in the study of orthog- 
raphy. Experience has shown that a pupil may be skilled in 
oral spelling, and make many mistakes in orthography in his 
letters and compositions. 

A third advantage is that by the Written Method the pupil 
will spell all the words in the lesson, while by the Oral Method 
he spells only part of the words. The Written Method thus 
gives a more thorough drill in orthography during the recita- 
tion than the Oral Method. It also affords a better test of 
the comparative skill of the members of the class, since all 
spell the same words. 

A fourth advantage is that it gives the pupil an opportunity 
to review the misspelled words. This is one of the most im- 
portant points of a lesson in orthograph3\ In an v ordinary 
spelling-lesson, the pupil can spell one-half of the words before 
looking at them ; it is the hard words which he is liable to miss, 
that it is most important for him to study. If he misses 
these words and is not drilled upon them till he can spell them 
correctly, he receives no advantage from the lesson. Bv the 



TEACHING ORTHOGRAPHY. lOO 

Oral Method, the teacher cannot tell what words eacli member 
of the class is unable to spell ; and it would be very inconve- 
nient for him to keep a list of the words that are missed in 
order that the}' may be reviewed b}^ the pupil. 

Another advantage is that it keeps all the pupils emplojed 
during the recitation and holds the attention of all. A por- 
tion of the class cannot be inattentive while the others are 
spelling, as is often the case in the Oral Method. It should 
also be remarked that the pupil who learns to spell by the 
Oral Method of recitation is actually learning orthography by 
seeing the words as he studies them, and that he depends in 
spelling on his memor}' of the form of the word, rather than 
upon the recollection of the order of the names of the letters. 

Having considered the character of the two methods of 
teaching orthograph}', we will now describe the manner of 
conducting recitations according to each. 

III. Written Method of Teaching Orthography. 

A written recitation in orthography may be conducted by 
using Slates, or the Blackboard, or Blank Books. The meth- 
ods with Blackboards and Blank Books are now the more 
generally- employed. We shall describe each. 

Ulaclihoard Method. — In an exercise upon the Black- 
board, the first thing is the preparation of the board. The 
pupils should erase all the work upon the part of the board to 
be used, divide it into equal spaces by vertical lines, and each 
pupil write his name at or near the upper part of the space he 
is to use. The erasing and spacing may also be done by a 
committee, if the teacher prefers. _ 

Writing the Words. — The next step is the writing of the 
words. The words should be written in vertical columns 
rather than in horizontal lines. Ordinary- words should 
])egin with small letters, and proper names with capitals. 
The}' should not be followed with any mark of punctuat'on, as 



156 METHODS OF TEACHING. 

no grammatical relations are to be expressed. Care should 
be taken that the writing be neat and legible. The I's should 
be dotted and the ^'s crossed, and care taken by the pupil to 
prevent any doubt as to the manner in which he intended to 
spell the word. The following couplet, familiar to many of 
the teachers of our public schools, presents a good practical 
rule : 

"Dot your i's and cross your i's, 
Close your o's and open your e's." 

Pupils may sometimes be required to divide words into s}^- 
lables by means of a h^q^hen. This will teach them the proper 
syllabication of words, a knowledge which is often of use to 
them in writing. A dash should not be used for this division ; 
too great a distance between the syllables destroys the natural 
appearance of the words. An advantage peculiar to the oral 
method is thus secured in the written method of orthography. 
The teacher may also occasionally require them to mark the 
accented syllables of words. 

Instead of each pupil writing the same word, the class may 
be divided into two sections standing alternately, by counting 
one^ two, one, two, etc., the one^s taking one word, and the 
two\s the following word. Or the sections may be formed by 
numbering one, two, three, four^, etc., the odd number's writing 
one word and the even numbers writing the next word. There 
are two advantages in this: first, while one section is writing, 
the teacher can be pronouncing a word for the following sec- 
tion; second, it removes the temptation of coi:)ying a word 
from a neighbor, as each pupil stands between those who are 
writing a different list from his own. 

Corrections. — After the words are written, the next thing 
is the correction of the words that have been misspelled. In 
making the corrections, the teacher spells the words, and 
the pupils notice whether they have written them correctly, 
marking the misspelled words. These may be marked by the 
figures, 1, 2, 3, etc., or by di-awing a line under the word, or 



TEACHING ORTHOGRAPHY. 157 

b}- placing a cross, X , after each misspelled word. The latter 
method is preferred. After the misspelled words have been 
marked, they should be counted, and the number of them 
written above or below the columns. 

The corrections should be made by the pupils rather than 
by the teacher. Each pupil may correct his own mistakes ; or, 
at a signal, they may all change places and each pvipil correct 
the work of another. Many teachers prefer the latter method, 
since it removes the temptation to deceive. I should fre- 
quently, however, use the former method, creating a moral 
sentiment in the class that will protect the pupils from deceit 
and thus strengthen their moral natures. 

Misspelled Words. — The next step is to take a list of the 
misspelled words. These words should be written in a blank 
book prepared for this purpose. The pupils should review 
these words as often as once a week, and there should be a 
final review of them at the close of the session. 

Use of Blank. Boohs. — Blank books, prepared for the j^ur- 
pose, may be used for writing the words instead of the black- 
board. The words should be written neatly with pen and 
ink. The method of writing is the same as that already de- 
scribed in using the blackboard. The corrections may be made 
by the pupils, but it is preferred that the books be handed to 
the teacher, and the corrections be made b}^ him. The pupil 
should then write a list of each day's errors in the latter part 
of the book. It will be well to begin such a list on the last 
page of the book, as the pupil cannot know how much room 
will be required for it. 

An advantage of this method is that a permanent record of 
the spelling exercises is kept. It is also more convenient to 
keep a record of the misspelled words than by the blackboard 
method. The method is especially recommended for the ad- 
vanced classes, and also when the classes are lai'ge. 

Use of Slates. — In using slates, the pupils write thei words 
on their slates, as in the former methods. Each pupil may then 



lo8 METHODS OF TEACHING. 

correct his mistakes as the teacher spells the words, or, at a 
signal, slates ma}- be exchanged, and one pupil correct for 
another. The misspelled words should be copied in a blank 
book at the close of the recitation. This method is more con- 
venient for copying the misspelled words than the blackboard 
method, though it has the disadvantage that the teacher is 
not able to see the words while the pupils are writing. It is 
now less used than either of the two previous methods. 

Dictation E,cercls€s. — Instead of always writing words 
abstractly in columns, pupils should often be required to write 
words as they occur in sentences. Such exercises may be dic- 
tated by the teacher, and are called Dictation Exercises. The 
teacher may form sentences containing certain words, and 
have pupils write as he dictates them ; or he may give them 
one or more words, and have them write sentences containing 
the words. He maj^ also read sentences and paragraphs from 
a book or a newspaper, and have them written. Pupils should 
be required to be careful about the use of capital letters, punc- 
tuation and quotation marks, etc. The corrections may be 
made as before explained. 

There are many advantages in dictation exercises. Thej'^ 
will teach pupils how to spell words correctly as they use them 
in writing letters, etc. They will be found more interesting 
to pupils than writing words abstractly in columns. They 
will also teach the pupils the meaning of such words as they 
may not understand, and show how to use them correctly. 
The}^ will afford pupils a practical exercise in composition, 
and teach them the correct use of capitals, punctuation 
marks, etc. 

IV. The Oral Method of Teaching Orthography. 

The Oral Method of teaching orthography is that which 
endeavors to fix the correct spelling of a word in the memory 
by calling the names of the letters. It should be remarked, 
however, tliat in reality this oral method is more a form of 



TEACHING ORTUOGFiAPHY. 159 

recitation than of learning orthography. Even when the 
pupil recites by this method, he is learning by looking at the 
words, as he studies his lesson. 

In describing the Oral Method of teaching orthography, 
there are several special poUits which require our attention. 
The first is the Position of the Pupil, the second is the Assign- 
iiK'iit of the Words, the third is the Method of Spelling, and 
the fourth is Spelling Matches. 

Position of Pupils. — The pupils while spelling may be 
either seated or standing. If seated, they should be as near 
one another as may be convenient. They should sit erect, 
witli their hands in their laps or on the desk, and their feet 
on the floor. If standing, thej' should be in a straight line if 
possible, their feet in a proper position, their toes on a line, 
their hands hanging naturall}^ by their side, or folded in front, 
or, in the case of verj- young pupils, behind their backs, to 
keep them out of mischief; the shoulders should be thrown 
slightly back, and the body erect in a natural and healthful 
position. 

Assignment of Words. — The words may be assigned regu- 
larly from head to foot, or to the members miscellaneously. 
The latter is best adapted to secure attention; but the former 
is necessary if the method of " trapping " is nsed. The words 
themselves should be selected miscellaneonsly, and not in the 
order of the book, to prevent pupils' calculating and preparing 
their own words. When a word has been spelled correctl}'', 
another word should be assigned; when a word is missed by 
a pupil, the word is to be passed to the next and continued 
from one to another until it is spelled correctly. 

Another method of assigning words is that in which the 
teacher does not indicate to the pupils when a word is mis- 
spelled, but goes on and assigns the next word as if the pre- 
vious word had been correctly spelled. Every pupil is required 
to watch the spelling of each word, and if the previous word 
has been misspelled, ho should spell it correctU* rather than 



160 METHODS OF TEACHLVQ. 

the word assigned to him. This is an excellent method to 
secure the attention of the class. 

A method somewhat similar to the preceding is for the 
teacher frequently to assign the word just spelled, to the next 
pupil, whether correctly or incorrectly spelled. This keeps 
each pupil attentive to the spelling of ever}^ word, for the 
teacher's "next" is no indication that the word is misspelled. 
It keeps a class wide awake, requires each one to spell men- 
tall}^ nearly every word, and gives a certainty of opinion and 
decision with respect to the orthography of a word. 

Another method is to allow the pupils to assign words to 
each other, beginning after the first with the final letter of the 
word last spelled. This is an excellent exercise for variety, 
and awakens a great deal of interest. It also aflTords pupils 
an exercise in thinking quickly of words. 

In assigning words, the teacher's rule should be, to pro- 
nounce the word but once. If a teacher is accustomed to 
pronounce sevei*al times; the pupils will become accustomed to 
requiring it ; if the rule is to pronounce but once, there will 
seldom be occasion to repronounce a word. I would depart 
from this rule only when, on account of some noise, or for 
other reasons, there was a good excuse for a pupil's not un- 
derstanding the word. When a word is missed, in passing it 
to the next pupil, it should not be repronounced ; each pupil 
should understand ever}' word assigned. Of course, with very 
young pupils, a little allowance must be made for circum- 
stances which may distract the attention. 

Again, the teacher should not depart from the correct pro- 
nunciation of a word to aid a pupil in spelling it. Thus he 
should not pronounce "sep-a-rate," or "ed-z-ble," etc., thus in- 
dicating the spelling of the word by a mispronunciation of it. 
This is sometimes done through sj'^mpathy, to keep a pupil 
from missing, but it is nevertheless wrong. If the pupil can- 
not spell the word without this help, he simply does not know 
how to spell the ^\ord and sliould fail on it. 



TEACHING ORTHOGRAPHY. 16 L 

Spelling the Words. — When the word is assigned, the 
pupil's first duty is to pronounce the word. The object of 
this is to see if the word to be spelled is distinctly understood. 
The next step is to name the letters of the word in their order, 
pronouncing the syllables, and pronouncing the entire word at 
its close. Pupils may also spell b}^ syllables^ or even by letters^ 
that is, each pupil spelling one s^^llable or naming one letter 
in a word. This latter method is on\y for variety, however. 

As a rule, I would require pupils to pronounce the syllables 
of words as they spell them. When so required, the^^ should 
pronounce the syllable even when it consists of but one letter, 
as in the word lin-i-ment, for often the name of the letter is 
not its sound in pronouncing the word. I would require also 
that the previous part of the word be repeated in connection 
with each new syllable ; as, l-i-n, lin^ *, e, lini, m-e-n-t, ment, 
liniment. With the more advanced pupils and with long 
words, it may be sufficient merely to pronounce each syllable 
as it is spelled, pronouncing the word at its close ; thus, l-i-n, 
lin, z, e, m-e-n-t, ment^ liniment. With the most advanced 
pupils, it will be sufficient, a portion of the time, to have them 
simply name the letters in their order, indicating the separa- 
tion of the s^dlables by pausing between them ; as, l-i-iv-i~ 
m-e-n-t, liniment. 

The pupils should speak in a natural tone of voice. Do not 
allow them to pitch their voices upon a high ke}-, and shout 
or drawl out the sounds. The " spelling tone," heard in many 
schools, is very objectionable. Neither should a pupil be al- 
lowed to mumble his Avords. Each element and syllable should 
be enunciated in a full, natm-al, and distinct tone of voice. 

Pupils should also be required to spell phonetically, that is, 
by giving the elementary sounds which compose words. 
Such an exercise belongs more particularly to pronunciation, 
and comes under the head of phonic analysis; but it will be 
convenient to have it also in the spelling classes. 

The Spelling' Match. — One of the most interesting and 



162 METHODS OF TEACHING. 

instructive exercises of the oral method is the spelling match. 
Its competitive principle is a stimulus for preparation ; and it 
carries with it all the excitement of contest and satisfaction of 
triumph that is felt in a game of base-ball or other contest of 
skill. We shall describe it somewhat in detail. 

The sides are usually chosen by two persons of about equal 
spelling ability, appointed by the teacher or selected by the 
class. These "leaders" or "captains" select the members of 
their sides, by alternate choice until all who are to participate 
are chosen. There are several methods of conducting the 
exercise, which we shall attempt to distinguish by character- 
istic names, and to describe. 

Spelling Doivn. — The usual method is for the opposing 
'parties to stand on opposite sides of the room, words being 
assigned to each side alternately. When a word is missed on 
one side, the person missing it takes his seat, and the word is 
passed to the opposite side, etc. The contest is decided by 
one side being "spelled down;" or by comparing the number 
left standing at the close of the match. 

Saving and Out. — A variation of this method, known 
among pupils as "saving and out," is that in which, when a 
word is missed on both sides, the side which at last spells it, 
saves those of its own number who have missed it from going 
out. Those on the opposite side, however, who have missed 
the word, take their seats. 

Passing Over. — Another method is that in which when a 
word is missed on one side and spelled on the other, those 
who missed it pass to the side which spelled it. A variation 
of this method is to give the leader of the side a choice of one 
of the opposite party. This method is objectionable on ac- 
count of the noise and confusion of passing over, and also for 
other reasons. 

Climbers. — Another method is to send the best speller of 
each side to the foot of the opposite side, and then assign 
words from head to foot of each side, the "climber" moving 



TEACHING ORTHOGRAPHY. 163 

towards head for every missed word that he spells. The side 
whose climber reaches head first, or at the end of the lesson is 
the nearest head, wans the victory. 

Cftainpious. — Another method is for each side to select 
champions who step out from their ranks, and like the ancient 
champions before a battle, engage in a personal contest, the 
teacher assigning words alternately to them until one of them 
misses and falls. The side spelled down first, or that has the 
least number standing at the end of the lesson, loses the battle. 

3Hxed Seatiuf/. — An excellent method is to have the mem- 
bers of the two sides stand or sit consecutively in one 
continuous line, the woi'ds being passed from head to foot, 
and a record being kept of the words missed by the members 
of each party. It has the advantage of preventing assistance, 
as each person has an opponent on each side of him. 

Half-way Line. — Another method is to have the pupils 
stand consecutively in a single line, each one having an oppo- 
nent at both sides; then mark a half-way line, assign the 
words from head to foot, allowing them to trap; and the 
part}^ which at the end of the exercise has the largest number 
above the half-way line, wins the victory. 

Keeping Tally. — Another method is' to have scorers aif)- 
pointed to keep a record of the words missed by both sides, 
as in a base-ball match, the contest being determined hy the 
tally. All of these methods possess advantages, and may be 
used to give variety and interest to the exercise. 

Y. General Suggestions in Orthography. 

There are several other points of practical importance in 
teaching spelling which we embrace under the head of General 
Suggestions. 

PapiVs Preparation. — The pupil should be required to 
make careful preparation for his spelling lesson. In stud3dng 
it, he should not depend upon calling the names of the letters 
and thus trying to fix them in his memory; but he should 



KU METHODS OF TEACHING. 

notice carefully the structure of the -words, and endeavor to 
stamp a picture of each word on his memor3^ He should 
always write the words of the lesson, even in preparing for an 
oral exercise, as he can in this way better fix them in the mind. 

Names of Common Things. — The teacher will find it an 
interesting and profitable exercise to require pupils to spell the 
names of common things. At the close of a lesson, the teacher 
may sa,y, To-morrow we will spell the names of all the things 
found in the parlor, or the kitchen, or on a farm, or in the 
barn, or in a carpenter's shop, or a blacksmith's shop, etc. 
The names of flowers, of trees, of articles of dress, of persons, 
etc., make an interesting and valuable exercise. 

Words often Misspelled. — The teacher should select words 
often misspelled, and drill the pupils upon them. With 
younger pupils these are the little words; us ^ thet^'e, their, 
which, lohere, until, some, many, piece, vei^y, any, inty, 
forty, right, great, every, neither, iceather, tvhether, etc. 
These are the words which they use in composition, in writ- 
ing letters, etc.; and they should be among the very first 
which the pupils learn to spell. It is a mistake to have pupils 
spelling words of three or four syllables which they very sel- 
dom use, while they cannot spell the little words of every-day 
life. Drill them also in words of like pronunciation and unlike 
oi'thography, a list of which can easil}' be found or made by 
the teacher. 

In all Branehes Attention should be given to spelling 

in all the branches. Frequently require pupils to spell some 
technical term in arithmetic or grammar, a name in geogra- 
phy or history, etc. We should make orthography specially 
prominent in the reading-lesson. This will beget in pupils a 
habit of looking at the structure of words, which will be of 
great value to them, for it is in this way that literary men 
and women become skilled in orthography. 

Association. — Words whose orthograph}^ it is difficult to 
remember may be associated with other words similarly 



TEACHING ORTHOGRAPHY. 165 

siDelled, whose orthography is remembered. Thus, a gentle- 
man who had a difficulty with jnece^ remembered whether the 
i or e came first by associating it with -pie in the expression, 
" a piece of pie." A lady who could not remember whether 
there were one or two e'.s before the a in agreeable^ was told 
to associate it with the fact that there were two agreeable gen- 
tlemen present Avhen she asked the question ; and slie after- 
ward had no difficulty with the word. A student remembered 
that there was no e before the m in judgment by the picture of 
the words on the blackboard with a line drawn by the teacher 
through the e {judgement) which the pupil had incorrectly put 
in it. A little mortification with the misspelling of a word, 
as many jDersons have experienced with the word separate^ 
will serve to impress the correct spelling. Some artifices 
like these are of value in those idiosyncrasies by which we 
are doubtful of special words. 

Words io Compose Words. — An interesting exercise in 
orthograph}' is presented by giving words for the pupils to 
compose other words out of their letters, using the letters no 
oftener than they occur in the given word. Thus, the word 
treation^iu. this way, will give over 100 words; Baltimore, 
over 200 ; comfortable, over 300 ; manufactory , over 500. A 
prize was offered by the Christian Union for the largest num- 
ber of words formed from subscription; the successful com- 
petitor made 1049 words. The pupils may also be allowed to 
use the letters of the word as often as they wish in forming 
new words. In this way a pupil of our Model School made 
out of the word Baltimore 2184 words. 

Rules for SpelUiKj. — English Orthography is so irregular 
that it acknowledges very little allegiance to rule. Most 
rules that can be given are subject to so many exceptions that 
it is usually easier to learn to spell words directly than to 
remember the rules and their exceptions. No one, therefore, 
can expect to learn to spell by rule. There are, however, a few 
rules that admit of very wide application, and are subject to 



16(3 METHODS OF TEACHING 

SO few exceptions that they may be used with advantage. 
The most important of these rules relate to the omission or 
retention of the final letter of a word on receiving a suffix. 
They may be stated as follows : 

1. Final e is omitted in adding a sufEx beginning with a vowel, and is 
retained in adding a suffix beginning with a coimmant. 

2. Final y when preceded by a consonant, is changed to i in adding a suffix ; 
but when preceded by a vowel, it is not changed in adding a suffix. 

3. A single final consonant is doubled on adding a suffix, — when the con- 
sonant is preceded by a single vowel, and the suffix begins with a vowel, 
and the final syllable is accented. 

4. The final consonant is not doubled, — if it is not preceded by a single 
vowel, or if the suffix does not begin with a vowel, or if the word is not 
accented on the last syllable. 

5. Of words ending in ceous or cious, — those which relate to mattei- end in 
ceous, and all others in cious. Silicious, sometimes written siliceous, is an 
apparent exception. 

These rules are subject to a few exceptions, but are regarded 
as convenient in i-emembering the spelling of the words to 
which they apply. For the exceptions, see How to Write Let- 
ters, by Prof. Westlake, who states the rules in a form similar 
to the above. 

False Orthographt/. — The use of false orthography has 
been recommended by some authors to aid the pupil in learn- 
ing to spell. Such exercises are supposed to bear the same 
relation to learning orthography as false s^aitax in grammar 
does to learning to speak and write correctly. The principle 
is that we. learn the right by seeing the wrong ; the correct 
usage by seeing the incorrect usage. It is, however, a ques- 
tion whether such exercises are not a disadvantage. Teach- 
ers who have used them say that pupils are liable to confound 
the correct and incorrect forms, that the picture of the mis- 
spelled word sometimes clings to the memory and becomes a 
model to mislead the pupil. If this be so, then false orthogra- 
phy should not be used Avith young pupils. With a class of 
advanced pui)ils it might be of advantage if used occasionally. 

Finally, cultivate an interest among your pupils in spelling, 



TEACHING OKTIIOGRAPHY. 167 

and manifest an interest in it yourself. Make your pupils 
feel that poor spelling is a disgrace; and lead them to see 
that correct spelling is a characteristic of a cultivated lady 
and gentleman. Relate to them instances of persons failing 
to secure positions on account of a mistake in orthography. 
Train them to the habit of noticing the orthography of words 
in their reading, for it is in this way that men and women 
really learn to spell. Remember that good spelling is taught 
only by careful observation and practice. 



CHAPTER VI. 

TEACHING READING OR ELOCUTION. 

READING", or Elocution, is the art of giving proper oi-al 
expression to thought and sentiment. It is the art of 
correct vocal delivery with the speaking tones of the voice in 
distinction from the singing tones, Reading and Elocution 
are very nearly synonymous, though the latter term is gener- 
ally applied to the higher departments of Reading. Silent 
Reading, or reading to one's self, is not included in the defi- 
nition, as this is merely seeing the thought through the words, 
and not oral delivery. 

Importance Reading is one of the most important 

branches in our schools. This importance ma}' be somewhat 
appreciated by comparing it with other branches, as arithmetic, 
grammar, music, etc. Many persons would rather be a great 
elocutionist than a great mathematician, grammarian, or mu- 
sician. The great actors have been as highly honored as the 
great musicians; Charlotte Cushman has perhaps as enduring 
a fame as Jenny Lind. The eminent orators stand as high in 
public appreciation as the eminent mathematicians ; though 
part of this eminence is due to the thought and sentiment ex- 
pressed, rather than to the deliveiy. Reading is a fine art, 
and should be regarded as a valuable accomplishment; with 
proper attention to it, we could make reading and reciting as 
popular in society as pla3ing the piano or singing. s 

Reading has been verj- poorly taught in most of our 
schools. In the colleges, until quite recently, no instruction 
whatever was given in deliver3\ In our seminaries and acad- 
emies, though there were special teachers of mathematics, 
natural sciences, languages, etc., any one was regarded as 

(IfiS) 



TEACHING READING OR ELOCUTION. 169 

competent to hear the reading classes. The pupils in our 
public schools were '"taught to read," but it was really a 
"calling of words" and not reading in its true sense. The 
best work in this branch has been done in our Normal 
Schools, and their influence in improving the methods of 
teaching reading has been wide-spread and beneficial. 

We should make a special study of reading, and endeavor 
to excel as teachers of it. Even for the teacher's own culture 
and success, it will be found of great advantage. Our influ- 
ence will depend almost as much upon the manner of our 
saying things, as on what we say. In social life, we render 
ourselves agreeable and increase our influence by an attractive 
and pleasing manner of expression. Business success depends 
largely on a person's address ; and influence in public life is 
to a large extent the result of a clear and forcible expression 
of thought. A public speaker should be a good elocutionist. 
The great orators were skilled in their delivery, as well ns 
clear and forcible in their style of composition. It is reported 
of Whitefield that he could move anaxidience to laughter or 
tears by the utterance of the word Mesopotamia. Demos- 
thenes and Cicero cultivated the art of delivery with the most 
assiduous care, and were masters of expression as well as of 
composition. 

3Iethocls of Teaching. — Methods of teaching reading may 
be discussed under three heads ; the Mental Element, the 
Vocal Element, and the Physical Element. 

The Mental Element is that by which we understand and 
feel what we read. It includes the Intellectual and the Emo- 
tional elements. The Intellectual Element is that by which 
we understand what we read. The Emotional Element is that 
by which we feel and appreciate what we read. Both of these 
are necessary conditions for correct and effective reading. 

The Vocal Element is that which pertains to the voice. It 
embraces Pronunciation and Modulation. Pronunciation is 
the art of giving correct utterance to individual words. It 



170 METHODS UF TEACIIIXG. 

embraces Articulation and Accent, both of which have been 
discussed. Modulation has reference to the variations of the 
voice in reading and speaking. It embraces Quantity, Com- 
pass, Quality, and Time, each of which has its appropriate 
subdivisions. 

The Physical Element is that which pertains to the bod}' 
and its members. It includes Breathing, Posture, Gresture, 
and Facial Expression. 

We shall discuss these three elements more fully than is 
necessary for ordinary common school work, though the 
teacher who understands these principles will be better qual- 
ified to give even primary instruction in reading. 

Primary Heading. — For primar}^ classes in Readiug we 
make the following suggestions: 

1. Require the pupils to be able to pronouiice words at sight. 
Require them to know the words at a glance, so that they can 
speak them in reading without hesitation or stammering. To 
secure. this, have the pupils pronounce the words before at- 
tempting to read. They may sometimes begin at the latter 
part of a paragraph and "pronounce the words backward." 

2. With the more advanced classes, before reading a new 
lesson, go over it and have the pupils pronounce all the un- 
familiar and difficult words. Some of these may be written 
on the blackboard to aid the pupil in remembering them. See 
also that they know the meaning of the words of the lesson 
before they begin to read. 

3. After the pupil can pronounce words at sight, particular 
attention should be given to the thoughts expressed. Have 
pupils state the thought in their own words. Require them 
to look at a sentence and tell you what it is about, and then 
read it. 

4. Require pupils to read m natural conversational tones. 
Do not allow them to use the unnatural tones so often heard 
in the reading of children. Discard, by all means, the well- 
known "school-room tone." Require the pupils to read in 



TEACHING READING 01! ELOCUTION. 171 

imitation of good conversation, remembering that conversa- 
tion is the basis of good reading. 

5. Attend carefully to articulation and pronunciation. Be 
careful to secure clear and distinct enunciation. Do not per- 
mit the drawling of the voice, nor the reading too rapidl3\ 
^e careful also to secure variety of tone, and to prevent 
monotony. 

6. Eri'ors may be corrected by calling on some pupils to 
imitate the reading of other pupils. It will call attention to 
defects that were not noticed and also cultivate the power of 
imitation. 

7. Let the class occasionally close their books and listen 
Avhile some one reads, and then request them to tell the 
substance of what has been read. Have them also point out 
mistakes and make suggestions for improvement. 

8. Do not go through the book too rapidl}^ In reading it 
is a good motto to " make haste slowly." Keep the children 
at a piece until they are pretty familiar with it. The better 
they know it, the better they can read it. 

9. See that children appreciate what they read. Let their 
little hearts be touched with such sentiments as can be appre- 
ciated by them. It needs a refined taste to read well; and 
the reading class presents a good opportunity to cultivate the 
taste. 

10. Have pupils stand erect, with the book in the left hand, 
the right hand hanging at the side, the feet in a proper posi- 
tion, etc. Permit no lounging or leaning upon the desk or 
against the wall, or standing in any awkward or ungraceful 
attitude. 

11. In their reading, let them be guided by two things; 
Imitation and Natural Expression. Let them imitate good 
models and read naturally, or as they would talk or tell the 
subject. Having presented these suggestions for primary 
instruction in reading, we proceed to a fuller discussion of the 
subject, as an art based on philosophical principles. 



172 MKTLIODS OF TEACHING. 



I. The Mental Element in Reading. 

The Mental Element in reading is that by Avliich we under- 
stand and feel what we read. It inclndes the Intellectual and 
Emotional elements. The Intellectual Element is that by 
which we understand what we read ; the Emotional Elementfs 
that by which we feel what we read. Both of these will be 
briefly considered. 

TIte Intcllectaal Element. — A pupil should understand 
what he reads. No one can read correctly what he does not 
fully comprehend. He may pronounce the words correctly, 
but unless he comprehends the thought he is endeavoring to 
present, it will be merely " calling words," not reading. This 
condition of good reading is frequently neglected. Pupils are 
allowed to read without having any idea of the meaning of 
what the}^ are reading. Pupils sometimes speak pieces with- 
out any clear conception of the ideas and sentiments ex- 
pressed. The artificial and unnatural style in which young 
persons read is largely due to the neglect of this principle. 
Most ridiculous mistakes are sometimes made \ty pupils in 
endeavoring to read that which they do not understand, or 
which the}'' misunderstand. 

Pupils should be required to prepare their I'eading lessons 
as they do other lessons. Every pupil should study his read- 
ing lesson. He should see that he knows the meaning of the 
words, of the idea intended to be expressed by the author, of 
the general character of the sentiment, of the meaning and 
force of the prominent allusions, rhetorical figures, etc. It 
will be well to go over the lesson and mark the emphasis, 
slides, varieties of voice, etc., appropriate to the difterent parts 
of the piece to be read. If a portion of it were entirely'^or 
partly committed to memorv, it could be read much more 
readily and correctly. It is said that the great orators studied 
their addresses so carefully that they knew just what words 
they were to emphasize, where to make a gesture, etc. 



TEACHING READING OK ELOCUTION, 173 

Teachers should examine their pupils to see that they under- 
stand the reading-lesson. They should ask them questions 
upon the meaning of words, upon the thought intended to be 
presented, upon tlie figures and allusions that may be used, 
upon the historical or biographical references, upon the gen- 
eral sentiment of the piece, and upon the style or character of 
the composition. Teachers who have not been accustomed to 
such an examination will be utterly surprised at the ignorance 
and thoughtlessness of pupils in this respect. Some very 
amusing and ridiculous mistakes could be given, illustrating 
the necessity of such questions. Pupils may often be required 
to give the sense of a passage or paragraph in their own lan- 
guage, to see if they understand it. Be especially careful in 
their reading of poetry, that it is not a sing-song of words, 
without an}^ true conception of the meaning. 

The teacher should explain what the pupil does not under- 
stand. He should explain the meaning of words, sentences, 
allusions, figures of rhetoric, etc., which the pupil has not 
understood. When the pupil meets such expressions as the 
"Archimedean lever," or the "Palladium of our liberties," as 
found in Washington's address, or the "Niobe of nations," as 
found in Childe Harold, etc., the teacher should explain the 
historical fact or mythological story from which they are 
derived, and show the force and beauty of the figure. So in 
reading poetr3^ ; when he comes to such passages as " The 
darkness falls from the wings of night," or "And Wind, that 
grand old harper, smote his thunder harp of pines," or" The 
Morn in russet mantle clad, walks o'er the dew of yon high 
eastern hill," etc., let the teacher call the attention of the 
pupil to the beaut3^ of the image and make his imagination 
picture it before the mind as it was seen by the poet who 
wrote it. The heart of the learner can in this way be thrilled 
with the emotion of beauty, the imagination be trained, and 
the literary taste be cultivated. 

The reading books should be adapted to the pupils. For 



17Jt METHODS OF TEACHINQ. 

young pupils, we need simple descriptions, lively narratives, 
and interesting conversations or dialogues ; for more ad- 
vanced pupils, essays, reflections, discussions, orations, etc., 
are appropriate. This principle is frequently disregarded. 
Many authors have completely failed in tlie adaptation of the 
reading matter of their books to the capacity and taste of the 
pupil. Only a few seem to have accomplished the difficult 
task of entering into the sphere of child-life, and adapting 
their writings to childreu. 

Teachers must also be careful to grade the books properly 
for the pupils. The general fault is that the books are too 
difficult for the-classes using them. The pupil is often in the 
Fourth Reader when he should be in the Second or Third 
Reader. In such cases the pupil should be put in a lower 
book if possible. If this cannot be done, the easier pieces 
should be selected, and the pupil drilled on them until he is 
familiar with all their difficulties. The more familiar a pupil 
is with a piece the better he can read it. 

The reading teacher should be a good scholar. In no class 
does a teacher require so much general culture as in reading. 
He needs a knowledge of history, mythology, rhetoric, etc., 
in order to explain the references, allusions, rhetorical con- 
structions, etc., in the lesson. The reading class, properly 
taught, can be made the most interesting and profitable class 
in the school. More can be done for literar}^ culture here than 
inany other study. Indeed, many a person has received his 
first impulse to literary culture in the reading class as taught 
by some earnest and enthusiastic lover of literature. 

TIte Emotional Element. — A pupil should not only un- 
derstand what he reads, but he should also feel and appre- 
ciate it. Literatui'e appeals to the heart as well as to the 
head. The reader should be susceptible to all the various 
phases of sentiment, and feel them when he is reading so that 
he may make others feel them. If the subject is pathetic, his 
heart should be touched with pity; if it is humorous, he should 



TEACiriVG READING OK ELOCUTION. 175 

appreciate the humor; if it is grand and sublime, he should 
feel the emotion of grandeur stirring in his soul. This point 
is of great importance in all the higher departments of read- 
ing, and demands the teacher's attention. 

Pupils do not usually feel or appreciate what they read. 
They will read one style of composition in just about the same 
tone and pitch as another, so that if you judged the composi- 
tion by the manner of reading, you could not tell whether 
they were reading a funeral sermon of Bossuet, or a humorous 
description by Mark Twain. There is no response to the 
touch of pathos or beauty, no heart-throb to the poet's line, 
or the orator's sentiment ; indeed there is often no more feel- 
ing than if a talking machine were repeating the words of the 
reading-book. 

The teacher should call the attention of the pupils to the 
sentiment, and endeavor to awaken an appreciation of it. By 
appropriate questions and explanations, he should endeavor 
to open the eyes of the pupil that he may see, and unseal his 
heart that he may feel, those touches of beauty and humor 
and pathos which throb in the poet's line, or live in the 
orator's phrase. He should give illustrations of the different 
kinds of sentiments, and show how the voice and manner 
should be adapted to express them. In a word, he should 
train his pupils so that they may feel what they read, as well 
as understand it. 

Reading books should be adapted in sfentiment to the age 
of the pupils. The grander sentiments of sublimity, patri- 
otism, etc., are not suitable to children. They cannot be 
expected to be much moved by a description of the " Sublimity 
of the Starry Universe," or the " Enjo^-ments of Content- 
ment," or the " Remorse for Neglected Opportunities," The 
pathetic and many forms of the humorous, however, will be 
readily appreciated. The narration of interesting events, of 
dangers in field or forest, of hairbreadth escapes, of the rob- 
bing of a bird's nest, of sorrow at the loss of a mother or 



176 METHODS OF TEACHING. 

sister, etc., will awaken their little hearts to intense feeling. 
The compilers of text-books on reading should bear this in 
mind, and govern themselves in their work accordingl}'. 

The teacher should not only be a good literary scholar, but 
he should also possess a cultivated taste. Refinement of 
mind, a heart to feel and appreciate the beautiful and good, 
will enable a teacher of reading to tpuch the hearts of his 
pupils and cultivate in them a refinement of taste which will 
improve both their character and their reading. The teacher 
of reading should therefoi'e take special pains, by the study 
of the fine arts and the cultivation of that which is beautiful 
and noble in human character, to acquire such refinement of 
taste and feeling as shall fit him for the highest attainments 
in his high art. 

IT. The Vocal Element in" Reading. 

The Vocal Element in reading is that which pertains to the 
voice. It is the fundamental element of the art of reading. 
The Mental Element is mei-ely a condition for good reading, 
and the Phj^sical Element an accompaniment of it ; but the 
Vocal Element is that which is immediately concerned in 
reading. It is the basis upon which the art is established. 

The importance of vocal culture in reading cannot be over- 
valued. The excellence of reading depends mainly upon the 
character of the voice. When the voice is harsh or hard and 
inflexible, it is impossible to read Avith artistic eff"ect. A full, 
rich, musical voice will chain the attention of an audience, 
independently of the sentiment expressed j and Avhen em- 
jiloyed in the expression of noble and soul-stirring sentiments, 
its influence is irresistible. 

Much of this excellence can be acquired by judicious cul- 
ture. Though some voices are by nature richer and more 
musical than others, yet careful training will remove man}^ 
defects and impai-t flexibility and sweetness in a remarkable 
degi'ee. Nearly every one is familiar with what culture and 



TEACHING READING OR ELOCUTION. 177 

training will do for a singer; and vocal culture is as necessary 
and useful to the reader as to the singer. The human voice, 
in the hands of a master, will attain to a wondrous strength 
and richness of tone. Practice also will give a person such a 
command over his voice and enable him to use it with such 
skill, that he can hold the attention of an audience by the 
music of his utterance, and thus deepen the impression of the 
sentiments he may express. 

The Vocal Element embraces four things ; Quantity^ Com- 
pass, Quality, and Time. These elements are usually included 
under the head of Modulation. Each of them will be consid- 
ered somewhat in detail. 

I. Quantity. — Quantity, as employed in reading, has refer- 
ence to the amount or volume of the voice. It is used by 
some elocutionists to mean the time occupied in pronouncing 
a word or syllable; but this is not the best or most accept- 
able use of the term. Quantity in reading is a general term 
including Force, Emphasis, Stress, and Slur. 

Quantity of voice is an important element of expression. 
Each sentiment has its appropriate quantity, and the quantity, 
if properly used, will indicate the sentiment. Thus, joy is 
expressed in a full torte, sorrow in a subdued tone ; modesty, 
humility, shame, doubt, mj-stery, etc., require soft and sub- 
dued tones. Anger declares itself in loud tones, confidence 
asserts itself with a full voice, secrecy softens the tone and 
speaks with muffled voice or whispered accents. 

Force. — Force is the quantity of voice used in reading or 
speaking. It is quantity as applied to vocal delivery. As 
used here it has reference to the standard force of the voice 
in reading or speaking. 

There are three degrees of Force ; Soft, Moderate, and 
Loud. Moderate Force is the ordinary force of the voice in 
reading and speaking. Soft Force is less force than the ordi- 
nary quantity ; and Loud Force is more force than the ordi- 
nary quantity. These are not fixed degi'ees of force, but 
8* 



178 METHODS OF TEACHING. 

merel}'' relative distinctions. Let the pupil be careful not to 
confound loud and soft with high and loiv, which are degrees 
of pitch. A mistake of this kind often leads the reader, when 
he designs to increase his force, to raise his voice to a higher 
pitch, tlius giving a higher instead of a louder sound. 

How Teach. — We should teach reading with respect to 
force by Exercises, Imitation, and Correcting Errors. 

Exercinea. — The Exercises recommended to cultivate force 
are as follows: 1. A frequent drill on the elementary sounds; 
2. A drill on sentences selected for the purpose; 3. Physical 
exercises to develop the general health and strength. 

In the drill on the elementary sounds, we slaould begin with 
a moderate degree of force, and then increase the force gradu- 
ally to the limit of loudness, being careful not to strain or 
overtax the voice. Having reached the louder tones, pass 
gradually from these to the softer tones. After some prac- 
tice in this way, the pupil may begin at the loud tones and 
pass to the softer ones ; or he may practice striking at once 
different degrees of force until he can give with ease and pre- 
cision any degree of force, from whisi)ering to shouting. 

Similar practice with well-selected sentences is also valuable. 
Let the same sentence be given with varied degrees of power; 
and let sentences be selected requiring variety of force for 
their natural expression. Such exercises, continued for a few 
months, will greatly enlarge the quantity of the voice and 
give the reader a command over it by which he can readily 
adapt it to the requisites of reading or speaking. 

In case of weakness of voice, arising from ill health or lack 
of physical strength, a course of gymnastics is recommended. 
The weak voices with which many clergymen are troubled, 
could be cured on the base ball ground or in the gymnasium. 
Theological students, or those preparing for public speaking, 
should take special pains to secure a vigorous constitution. 
Many a sermon could be rendered inore chxiueut and elfective 
in this way, and many a case of bronchitis avoided. 



% 



TEACniXG liEADIXG OR ELOCUTION. 179 

Imitation. — Since Reading is an art, and all art is largely- 
imitative, reading should be taught by imitation. In order to 
learn to read well we should hear good reading. The teacher 
should therefore be a good reader, that he may be a model for 
the imitation of his pupils. The teacher should read for his 
pupils, and have them imitate his manner of reading. He 
should be careful to avoid all errors of manner or style, or 
they will be acquired \)j his pupils. One can often tell who 
was the instructor of a reader b}^ his manner of reading. A 
teacher who reads well himself will usually have pupils who 
read well also; it is therefore of prime importance that the 
teacher of reading should be a finished and artistic reader. 

Principle. — There should also be some general principles to 
guide a pupil in reading. By a principle of reading, we mean 
some general law which can be readily applied to the partic- 
ular cases which we meet in discourse. Rules of reading have 
been criticised, and correctly so, for no one can read by rule. 
A principle, however, is more flexible than a rule, and will be 
of real value in learning to read. Of all the principles which 
we have seen we prefer those of Prof. Mark Bailey, as pre- 
sented in Hillard's readers. The principle for Force is as 
follows : 

Determine the standai'd force by the general spirit of the 
piece. If the general spirit is unemotional, the standard force 
is moderate ; if the general spirit is bold, noble, dignified, etc., 
the standard force is loud ; if the general spirit is grave, sub- 
dued, pathetic, etc., the standard force is soft. The pupil who 
grasps this principle and applies it intelligently, will find it 
of great value in reading. 

Correct Errors. — The teacher must notice carefully the 
errors of pupils and correct them. He should not merely call 
attention to these mistakes, but should train the pupils in 
cori-ecting them, until they have overcome the old habit and 
acquired the new. A few of the errors of force will be men- 
tioned. 



180 MLTIIODS OF TEACIIIXa. 

Some pupils read too softl}^ or with too little force. This is 
often the case with young ladies. The admiration of the " low 
voice in woman" is cai*ried to such an extent with many, that 
it is regarded as unladylike to read in public so as to be 
understood. Dr. Wickersham's description of the pupils of a 
young ladies' seminary who " undertake to entertain an audi- 
ence by reading compositions of which scarcely a word can 
be heard, and the listeners are compelled to be content, if they 
can notice a slight motion of the reader's lips, and, now and 
then, a change of position," represents what was formerl}'- of 
frequent occurrence ; and yet many of these girls out upon 
the playground would talk loud enough to be heard half a 
mile away. 

To correct the error of reading too softly, the teacher must 
notice its cause. Reading too softly is sometimes the result 
of a weak voice, sometimes of timidity, sometimes it is merely 
an affectation, and sometimes an unconscious habit. Correct 
the first by strengthening the voice, the second by aiding the 
pupil to acquire confidence, the third by a little judicious rid- 
icule, and the fourth b}^ showing the pupil the defect and 
inducing him to overcome it. A pupil who reads too softly 
may be placed at a distance from the teacher in reading. 
Such pupils may read dialogues, standing on opposite sides 
of the school-room,-or at some convenient distance from each 
other. 

Some pupils read too loud. Boys often make this mistake. 
Loud reading was formerly considered the best reading ; and 
boys would read almost as loud as they could shout. We can 
correct this error by showing them how unnatural and inap- 
propriate it is, and thus lead them to a natural method of 
expression. 

Most pupils do not adapt the force to the sentiment. This 
arises from the fact that they do not understand that to read 
anything is to express it naturally. This error needs the 
teacher's most careful attention. The pupil must be led to 



I 



TEACHING HEADING OR ELOCUTION. 181 

see that reading is natural oral expression, and that the force 
of the voice must be adapted to the sentiment expressed. 

Emphasis. — Emphasis is particular force applied to one or 
more words of a sentence. Its object is to give prominence 
and distinction to the important ideas. It brings out the 
meaning of an author, makes his thoughts and sentiments im- 
pressive, and gives beauty to expression as the play of light 
and shade does to a picture. A true emphasis keeps the 
attention of the listener in active sympath}^ with the thoughts 
of the speaker, gives full effect to all he utters, and makes a 
deep and lasting impression on the memory. 

There are two kinds of emphasis; Absolute and Antithetic. 
Absolute Emphasis is that which is applied to the prominent 
ideas of a sentence without any particular comparison with 
other ideas. Antithetic Emphasis is that which is used in 
contrasting ideas; as, " I said an elder soldier, not a better." 

Hotv Teach. — We teach Emphasis by means of Exercises, 
Imitation, Principle, and Correcting Errors. 

Exercises, etc. — For Exercises, drill the pupils on well 
selected sentences containing emphatic words. Dialogues will 
be found most suitable for 3'oung pupils. Repeating the ele- 
mentary sounds, emphasizing at intervals, is a good drill 
exercise. The teacher should also read for the pupils, placing 
the emphasis correctly, and require the pupils to imitate him. 
Some of the chapters in the Bible, as that of the Prodigal 
Son, so often incorrectly read, might be selected as an example. 

Principle. — No specific rule can be given for emphasis; it is 
a matter of judgment and taste. The principle of Prof. Bailej' 
will be of great advantage in applying emphasis. This prin- 
ciple is closely related to that of Force, and, as he gives it, is 
a part of the former. It is as follows : Having determined the 
standard force for the nnemphatic ideas, give more force to 
the emphatic ideas according to their relative importance. 

Correct Errors. — The teacher should constantly watch and 
correct the errors of pupils with respect to emphasis. The 



182 METHODS OF TEACIIIXQ. 

most common errors are those of incorrect and random em- 
phasis. Sometimes the emphasis is wrong because the pupil 
mistakes the sense ; this is corrected by calling attention to 
the important word. More frequently, the emphasis is applied 
at random, without any thought as to the prominent ideas. 
This error is often heard in the reading of the Bible and sacred 
hymns. It may be corrected by calling attention to the 
proper use of emphasis, and the reader's disregard of it. 

A ver}^ common fault in emphasis is the use of the circum- 
flex upon the emphatic word instead of the slide, as will be 
subsequently explained. The fault}- emphasis of the circum- 
flex can be removed by drill on appropriate examples, and by 
expedients adapted to individual cases. Another fault, often 
met with, is that of stiff and excessive emphasis, which can 
be removed by practice, the study of good models, and the 
culture of taste. 

Stress. — Stress is force applied to particular parts of mono- 
syllabic words or syllables. It is an unequal distribution of 
force on a syllable, and gives variety in the expression of a 
single word, as emphasis does in the expression of a sentence. 
There are five kinds of stress ; Radical^ Vanishing, 3Iedi'an, 
Gorivpound^ and Thorough. 

Radical Stress is force applied to the first part of a mono- 
s^^llabic word or of a syllable. It may be illustrated by pro- 
nouncing the words eat, out, etc. It is used in expressing 
anger, command, positive assertion, and in energetic senti- 
ments of all kinds. By it animals are awed into submission, 
and audiences are often startled, thrilled, and swayed. 

Median Stress is force applied to the middle of the word' 
or syllable ; as may be heard in pronouncing gold, far, leap, 
etc. It is used in expressing dignity, grandeur, solemnity, 
supplication, plaintiveness, etc. Median Stress gives beauty 
and expression to delivery. It is the natural utterance of 
thoughtful sentiment, and the swell is more or less prolonged 
as the feeling is moderate, or deep and full, lofty and sublime. 



TEACniXG READING OR ELOCUTION. 183 

It gives music to poetry, the spirit of devotion to sacred com- 
position, and the touch of eloquence to oratory. 

Vanishing Stress is force applied to the latter part of a 
word or syllable ; as may be illustrated in pronouncing hell, 
low, ring, etc. It is the expression of intense feeling deferred 
and accumulated upon the latter part of a word, as a child 
says, I wonH, I shan^t. This stress is used in expressing 
earnest purpose, determination, stern rebuke, contempt, aston- 
ishment, horror, etc. It is not so much an element of dignity 
as the median stress, yet it is an essential condition of high- 
wrought feeling and impassioned utterance. Without vanish- 
ing stress, oratory would often lose its manly energy of deter- 
mined will, and high-wrought resolution would fail of expres- 
sion ; while for the natural utterance of the elevated emotion 
and extreme passion of lyric and dramatic poetry, it is indis- 
pensable. 

Compound Stress is a combination of the radical and van- 
ishing stress. It is force applied on the first and last part of 
a word, as may be illustrated in the sarcastic utterance of the 
word yes. Compound Stress is used in expressing surprise, 
sarcasm, in Irish brogue, in snappish sentiments, etc. It is 
not an agreeable form of stress, and should be used only on 
those rare occasions which especially demand it. 

Thorough Stress is stress running through the entire word 
or syllable. It is used in expressing command, denunciation, 
bravado, and in exaggerated and mock heroic sentiment. 
When applied to continuous speech, it destroys the grace and 
delicac}' of utterance and becomes a sign of rudeness and vul- 
garit}". Judiciously employed, it is often a powerful weapon 
of oratory ; but when indiscriminately used it becomes mere 
ranting, and excites feelings of ridicule and disgust. 

How Teach. — Pupils should be drilled first on individual 
words until they can give them with the required stress, and 
then xipon appropriate pieces requiring different degrees of 
stress. Repeating the elementarj" sounds with varied stress 



184 METHODS OF TEACHING. 

affords an excellent exercise. The teacher should also pi*e. 
sent proper examples of stress for the pupils to imitate. In 
order to establish a principle, Bailey includes all varieties of 
stress under two heads, — Smooth and Abrupt. His principle 
is as follows : All pure and beautiful ideas should have smooth 
stress ; all abrupt ideas should have abrupt stress. The nat- 
ural language of stress which we have given in discussing each 
kind of stress will be a better guide in its use, however, than 
this principle. 

Slur. — Slur is a smooth, subdued, gliding movement of the 
voice applied to the less important parts of a discourse. It is 
generally used in what are called parenthetic passages. 

We teach slur by drilling the pupil in suitable exercises, by 
presenting good models for his imitation, and by correcting 
his errors. No principle can be given which will be of much 
advantage to the learner. 

II. Compass. — Compass has I'eference to the highness or 
lowness of the voice in reading or speaking. In speaking or 
singing, the voice moves between certain limits, above or 
below which it cannot utter sounds. The range included 
between these limits is known as the compass of the voice. 

In singing, the voice moves gradually up or dov>rn a series 
of eight sounds called the Scale. The distance between an}'- 
two points in the scale is called an Interval. The distance 
between any two successive sounds of the scale is called a 
second; the distance between the 3d and 4th and 7th and 8th, 
being half as large as the other intervals, are called minor 
seconds, while the others are called major seconds. The dis- 
tance from one to three of the scale is called a third, from one 
to four a /b?«r^//,, etc., and from one to eight an octave. A 
third which consists of two viajor seconds, is called a major 
third ; a third of one viajor and one minor second, is called a 
minor third. 

The voice may pass directly from one note of the scale to 
another, as in singing ; or it may slide from one degree to 



TEACHING READING OR ELOCUTION. 185 

another, as in speaking. Tlie former is called a discrete inter- 
val ; the latter a concrete interval. In the concrete interval, 
the voice rises concretely through the ditferent intervals, as in 
sliding the finger on a violin string. The discrete interval 
steps, as it were, from one tone to another, like the tones of 
the organ. The former, figuratively speaking, is a rising or 
falling stream of voice ; the latter is a voiceless space. 

The first sound of the scale is called the Key-note. The pitch 
on which a syllable or word begins, is called its Radical Fitch; 
the point at which the voice arrives by a concrete or discrete 
movement, is called its Concrete or Discrete Pitch, etc. The 
subject of Compass embraces three things ; Key-note, Slides, 
and Melody. 

Key-Note. — Key-Note in elocution is the standard pitch of 
the voice used in reading and speaking. It is of three degrees ; 
High, Low, and Medium. These are not absolute but relative 
distinctions of pitch. Different voices diflTer naturally in pitch, 
and what is medium to one voice, may be high or low to an- 
other; and the medium pitch of any one voice will range 
through several notes. 

Voices are of two general classes with respect to pitch ; 
men's and women's voices. These differ in pitch one octave, 
women's voices being an octave higher than men's voices. 
Women's voices are of two general classes ; Soprano, a high 
female voice, and Alto, a low female voice. There is also a 
voice, sometimes met with, between these two, called Contralto. 
The soprano is the finest voice for singing; but the alto and 
contralto voices are usually the most effective in reading. 

Men's voices are also of two general classes; Tenor and 
Base. Tenor is a high male voice; Base is a low, deep, male 
voice. There is also a voice intermediate between these, called 
Baritone. The base voice is the most impressive in reading 
and speaking, and is especially adapted to solemn and grave 
deliver}-, as in reading the church service, etc. The tenor is 
capable of more variety, and, while less impressive than the 



1S6 METHODS OF TEACIIIXG. 

base voice, is less tiresome to the listener. The baritone is 
often less musical than either of the others, and less servicea- 
ble either in reading or speaking ; though a rich and flexible 
baritone is the best of all voices for oratory. 

How Teach. — A pupil should be drilled on exercises to 
give him complete mastery over the pitch of his voice. First, 
he should practice singing the musical scale. Second, he 
shovdd be required to give the elementary sounds on different 
degrees of the scale, beginning at a low pitch and ascending 
gradually as high as he can speak with ease, and then gradu- 
ally descending to the lowest pitch. Third, he should be 
required to repeat sentences on different degrees of the scale, 
and to read selections which require variety of pitch. Such a 
drill will enrich the voice and give him complete command 
over its pitch in reading or speaking, 

Princijile. — Pupils should be led to see the relation of the 
different degrees of pitch to the different varieties of senti- 
ment. There is a natural relation between the pitch of the 
voice and the emotions of the heart. Deep feeling requires 
low tones ; J03'ful and elevated feeling requires a higher tone 
of voice; and sorrow and pit}', though requiring soft force, 
are also expressed by the higher notes of the scale. All ordi- 
nary and moderate emotions incline to the middle range of 
the scale. 

The general principle to guide in the adaptation of the pitch 
of the voice to the sentiment maj' be expressed as follows : 
Determine the standard pitch b}^ the general spirit of the 
piece ; if the general spirit is unemotional, the standard pitch 
is medium; if the general spirit is animated, joyous, or 
pathetic, the standard pitch is high ; if the general spirit is 
noble, grave, dignified, etc., the standard pitch is low. 

Correct Errorn. — There are several classes of errors in re- 
gard to pitch which require to be corrected. Many pupils 
pitch their voices too high in reading and reciting. This is 
especially the case with young lads of a jovous and livel}' tern- 



TEACniXG READING OR ELOCUTION, 187 

perament. It is also a common fault of teachers in explaining, 
to their pupils, in reading problems in arithmetic, etc. Many 
public speakers speak in too high a key, and too many per- 
sons do so in ordinary conversation. A high pitch is unpleas- 
ant to the cultivated ear, and is totally inadequate to the ex- 
pression of sentiments of veneration, dignity, or sublimity. 

A few pupils pitch their voices too low, though the fault is 
somewhat rare in school. A few public speakers also habitu- 
ally use a grave and hollow tone of voice, and thus impart a 
deep and sepulchral solemnity to all subjects alike. 

Most pupils and readers do not adapt the pitch to the sen- 
timent, reading all things with about the same degree of pitch. 
Falling into this habit, they use the same tone in all varieties 
of subjects, and read a notice of a Sunday-school celebration 
with as deep a solemnity of tone as they would use in 
announcing the death of a member or preaching a funeral 
sermon. 

Many, again, do not discriminate between pitch and force. 
Tell them to read lower, and they read softer, and perhaps 
pitch the voice higher. All errors should be corrected with 
great care. The pupil should be taught to see the relation 
between the pitch and the sentiment to be expressed, and then 
be required to adapt the voice to the nature of the piece read 
or recited. Those who speak habitually too high may be 
given a pitch of the scale to use as the key-note of a piece. 
Some of the ancient orators used to have a person back of the 
stage to sound the key-note as they passed from one part of 
their speech to another. 

Slides. — Slides, or Inflections, are variations of the pitch 
of the voice on different words or syllables of a sentence. No 
two siTccessive words or syllables of a sentence are usually 
uttered with the same pitch of voice ; and the pitch of the 
voice in ordinary natural expression usually varies in pro- 
nouncing each word and syllable. We begin a word with a 
certain pitch and end it in either a lower or a higher key. In 



188 METHODS OF TEACHING. 

natural expression, the voice moves concretely on words and 
syllables, through the interval from one degree of pitcli to 
another. Such variations of jjitch are called Slides. 

Slides are of three difterent kinds ; Rising Slides, Falling 
Slides, and the Circumflex. The Rising Slide is an upward 
slide of the voice ; it is often indicated by the acute accent 
('). The Falling Slide is a downward slide of the voice ; it is 
often indicated by the grave accent C). The rising inflection 
denotes hesitation or incompleteness of expression ; the falling 
inflection expresses decision and completeness of expression. 

The Cii'cumflex is a union of the lising and falling inflection. 
It is called Direct when the first interval ascends ; Inverted 
when the first movement descends. It is said to be Equal 
when the two slides are of the same degree, and Unequal when 
they are of different degrees. It is called Single when two 
intervals only are joined, as (V); and Double, when there are 
more than two, as (w). 

The use of slides and inflections is to give variety, beauty, 
and significance to speech. In connection witli force, they 
constitute emphasis, and thus give prominence to the emphatic 
ideas. In emphasis, it will be noticed, we have not only 
more force, but longer slides. Slides give variety to speech, 
for without it our reading would be monotonous and weari- 
some. They add the charm of melody or music to our utter- 
ances, and thus render our reading or spealiing more pleasing 
to the ear. 

Slides maj"- be of various degrees. Thus, the voice may 
vary a second, a third, a fourth, etc., as fiir as the octave. 
The Second is the rise or fall of the voice between any two 
degrees of the scale. Seconds are both major and minor, as 
previously explained. The term second, in reading, is usually 
applied to the major second. Thirds are also both major, as 
from the first to the third of the scale, and minor, as from the 
sixth to the eighth of the scale. 

The Second is tlie basis of correct and agreeable elocution. 



TEACHING READING OR ELOCL'TION. 189 

It is more used than any other interval, being appropriate to 
those parts of discourse which convey the plain thoughts of 
the speaker rather than those which express passion and ex- 
citement. The second is the least obtrusive interval of the 
scale, and is the simple sign of the unexcited sentiment of 
wisdom and truth. " The simple rise and fall of the second," 
says Dr. Rush, " and perhaps its wave, when used for plain 
narration, or for the mere statement of an unexcited idea, is 
the only intonated voice of man that does not spring from a 
passionate or an earnest condition of his mind." 

The slide of the Third is used for more earnest and ani- 
mated discourse than the second. The Downward Third ex- 
presses considerable feeling, though somewhat subdued and 
dignified. In simple narrative, it is often used with the sec- 
ond, in giving emphasis to the prominent words. The Rising 
Third is used in asking questions, and also for emphasis. It 
is the sign of interrogation in its most moderate form, and 
denotes but little earnestness or animation in the inquiry. 
The Minor Third is used in the emphatic words of pathetic 
utterance; as " Little Nell was dead. She died last night." 

The slide of the Fifth is used for very earnest and animated 
discourse. The Downward Fifth is employed in expressing 
surprise, admiration, and dignified command. It indicates 
strong emotion, but under the influence of the will and with- 
out the excitement of passion. The Rising Fifth is used for 
earnest interrogation, or for the emphatic expression of in- 
quiry or doubt. Yery few inquiries need a longer slide than 
the fifth. Any larger interval, on account of the difficulty of 
managing the voice, loses instead of gaining in force of ex- 
pression. 

The Octave Slide is used for the most earnest and animated 
discourse. The Falling Ociave expresses the highest degree 
of admiration or astonishment, and the ,most positive com- 
mand. Yery few pieces of composition require the octave, 
and in all ordinary utterances it would seem exaggerated and 



190 METHODS OF TEACHING. 

inappropriate. The Rising Octave expresses tlie most forci- 
ble degree of interrogation and of emptiasis on a rising inter- 
A'al. It is appropriate for tlie expression of contempt, mirth, 
raillery, and of peevish or indignant argument. When em- 
plo^'ed in ordinary or moderately earnest discourse, it be- 
comes ludicrous. Slides on the other degrees'of the scale are 
so seldom used that the}"^ are not described. 

How Teach. — Pupils should be drilled on the slides until 
they can give them readily of any kind and degree. Tlic 
vocals of the list of the elementary sounds, may be used -for 
this purpose, and also well selected sentences. Some good 
teachers use the violin in training the ear and voice in the 
matter of slides. The teacher, of course, should be able to 
give them well himself as a model for the imitation of his 
pupils. 

In order to apply a principle with respect to slides, all ideas 
may be divided into two classes ; positive ideas and negative 
ideas. Positive ideas are those which are used in affirming, 
denying, or making an inquiry in a positive form. Negative 
ideas are those which do not affirm or deny positively, which 
are in contrast with positive ideas, or which are used in aslv- 
ing a direct question. The former denote something com- 
pleted and definitely laid down; the latter indicate something 
incomplete, unfinished, or held up for further consideration. 
Such ideas have been regarded as direct, while those whicli 
are neitlier positive or negative have been called "crooked 
ideas," as those of jest, sarcasm, irony, etc. 

The general principle is, — All positive ideas should have 
the foiling slides ; all negative ideas should have rising slides ; 
and all crooked ideas should have the circumflex slides. 
Thus, all assertions or denials or questions containing a 
spirit of assertion or denial should have downward slides; 
all questions desiring an answer should have rising slides; 
while iron}', ridicule, insinuation, etc., require the circumflex 
slide. 



TEACUING READING OR ELOCUTION. TJl 

Tlie degree of the slide is determined by the nature of the 
sentiment. Unemotional pieces have short slides ; bold, dig- 
nified pieces have long slides. Very pathetic pieces require 
minor slides. These principles govern the majority of cases; 
but it should be remembered that the slide is largely subject 
to the demands of variety, melody, and to the relations of the 
different parts of the sentiment expressed. 

Melody. — Melody is a series of simple sounds so A'^aried in 
pitch as to produce a pleasing effect upon the ear. Melod}^ in 
reading is an agreeable variation of the pitch of the voice on 
and between the successive words and syllables of a sen- 
tence. It will be noticed that in natural expression there is 
a difference of pitch between words and syllables as well as a 
variation of pitch on them. The pitch of voice at which any 
word begins is a little lower or higher than the pitch at which 
the previous word ends. The term melody includes this varia- 
tion, and is also generally used to embrace the entire variation 
of the pitch of the voice in reading or speaking. 

The object of melody is to give beauty and variety to read- 
ing. It is the musical element of speech, and imparts a grace 
and charm to utterance, preventing monotony, and giving 
delight to the ear. Its absence leaves the wearisome effect of 
the unvarying monotone. It also enables the voice to rise or 
fall gradually on the unemphatic words, that it may have an 
opportunity for longer slides on the emphatic words. 

There are two distinct kinds of melody; Diatonic and Semi- 
tonic. Diatonic melody is a variation of a major second on 
and between successive words and S3dlables, Semitonic mel- 
ody is a variation of a minor second on and between suc- 
cessive words and syllables. The absence of melody pro- 
duces Monotone. Monotone is a sameness of pitch on and 
between successive words and S3"llables. 

Diatonic melody is used for the expression of all sentiment 
except the very pathetic or sublime. It indicates manly con- 
fidence and the self-reliance of truth. Semitonic melody is 



192 METHODS OF TEACHING 

used in very pathetic discourse. It expresses complaint, pity, 
grief, plaintive supplication, and the like. A misplaced use 
of the semitone leads to whining. It is diflicult to give semi- 
tonic melody with artistic efiect ; and when overdone, it 
awakens feelings of the ludicrous. 

The Monotone is used in expressing grandeur of thought 
and sublimity of feeling. It is used in expressing fear, vast- 
ness, majestj^, power, etc., sentiments which seem to partially 
obstruct or overawe the powers of utterance. The effect pro- 
dued by it is deep and impressive. When properh' em- 
ployed, the reading will be characterized by a solemnity, 
dignity, and grandeur, entirely in harmony with the senti- 
ments expressed. 

Cadence. — Melody gives rise to what is called the Cadey\ce. 
Cadence is the closing tone of a sentence. The completion of 
a thought is expressed, not only by the long pause w^hich takes 
place at the end of a sentence, but usually b}' a ftilling of the 
voice on the closing words to a lower pitch than that which 
prevailed in the body of the sentence. This closing descent 
in the tone is used to prevent the abruptness and irregularity 
of sound which would be produced by continuing the prevail- 
ing pitch to the close of the sentence. It is a prophecy of a 
close, prepares the mind for it, and thus avoids that surprise 
which would be at variance with both harmou}?- and meaning. 

The note to which the cadence falls and the space through 
which it descends, are dependent on the emotion which is to 
be uttered, or on the length or complication of the sentence. 
In strong emotion, the cadence is often both abrupt and low; 
as, " Let us do, or die." In gentle emotion, the cadence is 
gradual and moderate; as, "How sweet the moonlight sleeps 
upon this bank." In short sentences, where the emotion is 
slight, the fall is slight; as, " Night brings out stars, as sorrow 
shows us truth." In long sentences, the fall is more obvious 
and begins further from the close. 

How Tench. — Pupils should be drilled on the elementary 



TEACHIXO READING OK ELOCUTIOX. 193 

sounds and suitable exercises until they are familiar with 
melody. The teacher should be skilled in it himself, that he 
maj^ present suitable models for imitation. The principle is 
indicated above in speaking of the adaptation of the diflerent 
kinds of melody to the various kinds of composition. 

Principle. — We determine the melody b}' the general spirit 
of the piece ; all ordinary sentiment requires diatonic melody; 
ver}^ pathetic sentiment should have semitonic melody ; and 
very sublime discourse may be given with the monotone. 
To allow for emphasis we should let the voi.ce ascend on the 
unemphatic parts of the discourse so that we may have room 
to slide downward on the emphatic ideas. 

Correct Errors. — Some of the more common faults of 
cadence are the following : Delaying the fall of the voice till 
the last word or words of the sentence, and dropping at once 
from a preceding uniform tone. This is a common fault with 
children, or with pupils reading what they do not understand. 

Falling very low in the cloning 2^hrase. This fault is con- 
tracted by reading only grave and formal selections, and is 
frequently heard in the pulpit, and from young people who 
imitate the ministerial style. 

A gradual sliding downward from the beginning of the sen- 
tence. Some speakers or readers commence a sentence on a 
high note with full force, and gradually lower the pitch and 
diminish the force in the progress of the sentence, until the 
tone has nearly died away at its close. This fault is often 
heard in the pulpit. The pupil's attention should be called to 
anyone of these faults to which he is subject, and care be 
taken to correct the error. 

III. Time. — Time has reference to the fastness or slowness 
in reading or speaking. It includes two things ; Movement 
and Pauses. 

Movement. — Movement is the rate with which we read or 
speak. There are three degrees of movement ; Fast, Slow, 
and Moderate. These of course express relative rather than 



194 METHODS OF TEACHING. 

absolute degrees of time. Some writers also make the dis- 
tinction of Very Fast and Very Slow. 

Moderate Rate is the ordinary rate used in speaking or 
reading. It denotes self-possession, a complete command of 
one's powers, and an unexcited state of feeling. It is suitable 
to unimpassioned language, and is employed in narrations, 
descriptions, and didactic composition. 

Fast or Rapid Movement is that which is quicker than mod- 
erate rate. It is characteristic of gay, exhilarated, and joyful 
feelings ; and indicates some excitement of mind. It is used 
in giving utterance to all })layfal, humorous, and mirthful sen- 
timents, in excited argument, and also in expressing indigna- 
tion and fear. Very quick or rapid movement is expressive 
of haste, alarm, confusion, and extreme terror. 

Slow Movement is a slower rate than moderate. It is sug- 
gestive of repose, grandeur, majesty, vastness, power, and 
splendor. ]t is used in expressing the deeper emotions of 
grief, reverence, grandeur, sublimity, etc., and gives dignity 
and impressiveness to discourse. Very slow movement is 
employed in expressing the very strongest and deepest emo- 
tions ; as, horror, awe, profound reverence, solemnity, adora- 
tion, etc. It is especially suitable to many parts of the Bible, 
and to the discussion of many sacred themes. 

Hoiv Teach Drill pupils on suitable exercises, so that 

they may be able to have a complete command over their 
voices with respect to rate. Like a good musician, they 
should be able to read rapidly or slowly at pleasure. They 
must be led to see that in order to read slowly, the voice is 
to be prolonged on the vowel sounds of words, and they 
should be drilled until they can adopt an}'- rate at pleasure. 
The importance of such drill appears in the fact that it is 
more difficult to command the rate of reading than one Avouhl 
naturally suppose. The teacher, of course, should be able to 
pi-esent suitable models for imitation. 

Principle. — The i)riuciple for rate is as follows: Deter- 



TEACHING READING OR ELOCUTION. 195 

mine the standard rate by the general spirit of the piece. If 
the general spirit is unemotional, the standard rate is moder- 
ate; if the general spirit is animated, joyous, gay, etc., the 
standard rate is fast ; if the general spirit is bold, grave, dig- 
nified, etc., the rate is slow. Taking the standard rate for the 
unemphatic words, give additional time to the emphatic ideas, 
according to theif relative importance. 

Correct Errors. — The teacher must also be careful to cor- 
rect the errors of pupils with respect to rate. Most pupils 
read too fast. This may be corrected by leading them to 
dwell on the vocal sounds of the words. With very young 
pupils concert reading is a useful exercise, as they usually read 
more slowly when pronouncing the words together. Nearly 
all young speakers speak too rapidly in debate and declama- 
tion, and rapid speaking is a very general fault of extempor- 
aneous speakers. 

A few pupils read too slowl}', prolonging the words into a 
drawl. Such must be drilled to speak their words more 
quickly. Have them shorten the vowel sounds of words. 
Let the teacher give them lively sentences to read, and en- 
deavor to give vivacity and animation to their style. 

Nearly all pupils fail to adapt the rate to the sentiment, 
reading all kinds of discourse with the same rate. This must 
be corrected by calling attention to the relation of rate to sen- 
timent, and by unremitting drill. 

Pauses. — Pauses ai'e cessations of the voice in reading and 
speaking. They are the intervals between the utterance of 
words, clauses, sentences, and paragraphs, which correspond 
with and mark the divisions of meaning. 

There are two kinds of pauses ; the Grammatical and the 
Rhetorical. The Grammatical Pauses are those which indicate 
the logical or grammatical relation of the ditlerent parts of the 
discourse; they are represented by the punctuation marks. 
The Rhetorical Pauses are those which are required to bring 
out the sense or express the sentiment of a discourse; they 



196 METHODS OF TEACHING. 

are not marked, but are determined bj^ the sense of the piece 
and the judgment of the reader. 

Pauses are of great importance in reading and speaking. 
They are required both for ease of utterance and for clear and 
emphatic expression. They are useful to both the reader and 
the listener. To the speaker the rhetorical pause is necessary 
for breathing after uttering a succession of sounds embracing 
at least one word which demands a great impulse of the 
organs, and which partiall}' exhausts the suppl}^ of breath. 

The rhetorical pause is specially important to the listener. 
A proper pause at the end of a sentence, rests the mind of the 
hearer, and gives it time to dwell a moment upon the idea or 
sentiment presented. A pause after an emphatic word gives 
the mind an opportunity to linger on the idea and receive the 
full impression from it. As some one remarks, it gives time 
for the idea " to soak in" the mind of the hearer. It is thus 
true, in more senses than one, that " a pause is more eloquent 
than words;" and that though "speech ma}^ be silvern, silence 
is golden." 

How Teach. — Pupils should be drilled in exercises to ac- 
quire the right use of pauses. Show them the necessity and 
use of the rhetorical pause. Make them see that the length 
of the pause depends on the sense, and not on the punctua- 
tion. The old method of counting one at a comma, two at a 
semicolon, etc., is entirely objectionable. Show them also 
the use of the emphatic pause, and drill them in using it. 
Let the teacher give correct models, and correct all errors. 

Principle. — -The length of the pause depends on the nature 
of the discourse spoken or read. In unemotional composition 
the pauses are moderate; in energetic and impassioned utter- 
ance the pauses are long in order to give im])ressive emphasis; 
in strong and excited utterance the}' are often short and irreg- 
ulnr. Awe, solemnity, grandetir, etc., require long pauses, 
both at the end of sentences and for emphasis. 

Pause in Poetry. — The measured character of verse requires 



TEACHING READING OR ELOCUTION. 197 

certain pauses not used in prose. These are called the Poetical 
or Harmonic pauses. The Final pause is a short pause often 
used at the end of a line to marlv its close. The Caesural 
pause is that which is used to divide a line into equal or un- 
equal parts. The Demi-cnesural pause is a short pause which 
is sometimes used to divide the parts of the line already 
divided by the caesura. The rhetorical and caesural pauses 
usually coincide. When no pause is required, either by the 
punctuation or the sentiment, the harmonic pause should not 
be observed. 

Reading Poetry. — The chief faults to be avoided in reading 
poetry are the following: 1. Too rapid utterance, by which the 
effect of the verse is lost to the ear ; 2. A plain and dry articu- 
lation, which, though it may bring out the meaning, does not 
indicate the beauty of the sentiments and the rhythm ; 3. 
A mechanical observance of the harmonic pauses, without 
regard to the meaning; 4. A mouthing and chanting tone, pro- 
ducing the effect of bombast and mock solemnity ; 5. A sing- 
song style, as frequently heard in the school-room. 

Poetry should be read a little more slowly than prose, with 
a moderate prolongation of vowel and liquid sounds, a slight 
degree of musical utterance, and with an exactness of time, as 
indicated by the nature of the verse and the emotion ex- 
pressed. The utterance should indicate the metre but should 
never render it prominent. 

IV. Quality. — Quality of tone has reference to the kind of 
voice used in reading and speaking. It is one of the most im- 
portant elements of vocal expression. The tone itself, inde- 
pendent of the words used, is expressive of thought and feel- 
ing. Tone is the language of the heart ; the soul can be 
thrilled by the utterance of melodious and varied sound. A 
rich, sweet voice will hold the attention of an audience, even 
when there is no especial interest in the thought expressed. 
A pleasing voice will cast a charm of feeling and interest 
around the dullest composition. 



193 IIETHODS OF TEACHING. 

All the varied tones which can be uttered b}' the human 
voice have been embraced under six classes ; Pure, Orotund, 
Tremulous, Aspirated, Guttural, and Falsetto. These differ 
in different persons in accordance with the natural (juality of 
the voice, yet they represent distinct characteristics of the 
voice of each individual. 

Pure Tone is a pure, clear, round tone of voice. It is the 
ordinary tone of a good natural or well-trained voice. All the 
breath is vocalized, and the tone is produced by a verj' slight 
resonance in the head. It is appropriate to all kinds of dis- 
course not strongly emotional. 

Orotund is a full, deep, round, chest tone of voice. It is 
produced by a greater resonance in the head and chest, and 
requires a depression in the larynx, an opening of the throat, 
extension of the mouth, and expansion of the chest. It is 
appropriate to the expression of sentiments of dignity, 
grandeui', etc. It is employed in reading epic and dramatic 
poetry, and is indispensable in oratory. 

Orotund quality admits of three degrees ; Effusive, Expul- 
sive, and Explosive. Effusive Orotund is used in the utter- 
ance of sentiments of solemnit}' and pathos, when mingled 
■with grandeur and sublimit}'. It is also the appropriate tone 
of reverence and adoration. 

Expulsive Orotund belongs to earnest and vehement decla- 
mation, to impassioned emotion, and to any sentiment uttered 
in the form of shouting. Explosive Orotund is the language 
of intense passion. It is heard when the violence of the emo- 
tion seems beyond the control of the will, as in a sudden 
ecstasy of terror or anger. 

Tremulous Tone is a vibratory tone of voice. It consists 
of a vibration of the pitch of the voice in the utterance of a 
■word. It is used in expressing pathetic sentiments, in grief, 
pit}'^, sj-mpath}^, tenderness, etc. ; in suppressed excitement; 
in the trembling tones of old age, and occasionally in the 
exuberance of joy. A slight tremor often adds a charm to 



TK.\.CHIXG READING OR ELOCCTIOX. 199 

utterance, as the tremula in singing and violin playing does to 
music. It should, however, be used with discretion, being 
careful that it is not ovenione, when it savors of affectation. 
Dropping in now and then unexpectedly on expressive or 
tender words, it produces a very fine effect. 

Aspirated Tone is a whispered articulation, or a speaking by 
articulatiog the breath rather than the voice. It is used to 
give increased intensity to the utterance of the various emo- 
tions. It impiarts an air of mystery to a subject, and is thus 
used in expressing wonder, fear, and in circumstances where 
the voice is awed into silence. It is sometimes used in giving 
utterance to scorn, contempt, rage. etc.. where the intensity 
of feeling seems to choke or destroy the power of vocal utter- 
ance. 

The Guttural is a deep throat tone of voice. It is a depth 
of utterance so low as to pass b^ond the range of pure tone. 
It is used in expressing hatred, contempt, loathing, etc. 

The Falsetto is that peculiar tone heard in the higher 
degrees of pitch after the natural voice breaks or apparently 
transcends its range. It is used in the expression of extreme 
surprise, mockery, etc., and in the emphatic scream of terror, 
pain, etc. The most common use of it is with men in imitat- 
-~r female voices. 

Soir Teach. — Drill the pupils on exercises until they can 
readily give all the various kinds of tone. I^ad them to see 
the adaptation of the tone to the sentiment. Correct all 
errors in respect to the quality of the voice. If there are any 
natural defects of quality, point out the errors and endeavor 
^o have the pupils correct them. Have them imitate the 

icher, and apply the principles. The principles are given in 
ihe statements of the natural relation of the quality to the 
sentiment to be expressed. 



200 METHODS OF TEACHING. 

III. The Physical Element in Reading. 

The Physical Element is that which pertains to the body and 
its members. It is, as it wei"e, tiie addition of visible lan- 
guage to oral expression, and is thus used to give emphasis 
and impressiveness to the spoken words. It includes Breath- 
ing, Posture, Gesture, and Facial Expression. 

I. Breathing. — In order to read or speak well one must 
know how to breathe correctly. It is an element of great , 
importance, and one which has been greatly neglected. Many 
public speakers ruin their voices merely because they do not 
know how to breathe. Teachers' voices " give out" because 
they make the muscles of the throat do the work of the sides 
and waist. Preachers are on the retired list with bronchitis 
who might have preached half a century, if they had known 
how to breathe properly. We present the following sugges- 
tions upon this subject: 

How to Bi'eathe. — Breathe deeply. Some people breathe 
merel}'' witTi the upper part of the lungs. Let the entire lungs 
be brought into action. Breathe all the way down to the waist. 
Let the diaphragm be lowered, let the muscles of the back and 
the sides be brought into action, and let the waist be enlarged, 
even at the sacrifice of tight clothing and a false ideal of 
beauty. Such an exercise will be of great value to weak 
lungs as well as to Aveak voices. 

Use no more breath in speaking than is needed. Yery little 
breath is vocalized in speaking or reading, as may be seen by 
holding a piece of tissue paper hung by a silken thread, before 
the mouth, when speaking. The paper will scarcely move 
except in uttering the aspirates. Let the breath, therefore, 
be used with economy to insure ease and freedom of utterance. 
There is no need of pupils getting out of breath in reading or 
speaking, and the puffing and blowing of some speakers is not 
onl.y unnecessary but ridiculous, reminding one of the spout- 
ing of a porpoise. 



TEACHING READING OR ELOCUTION. 201 

Be carefal not to mix the breath with the voice. This is a 
fault occasionally met with among young pupils, and is a 
serious error in delivery. " Every tone," says Madam Seller, 
"requires for its greatest possible perfection, only a certain 
quantity of breath, which cannot be increased or diminished 
without injury to its strength in the one case, and its agreea- 
ble sound in the other." The use of too much breath mars 
the beauty of uttei'ance and exhausts the reader. 

In breathing, the air should be inspired through the nose, 
and not through the mouth. A speaker who takes in air 
through his mouth will find his throat becoming dry by the 
evaporation of the mucus, or natural moisture with which 
nature lubricates the vocal organs. Besides, if there are any 
irritating particles in the air, they will produce an irritation 
and titillation in the throat. It has been found that those 
persons who, during sleep, breathe through the mouth instead 
of through the nose, are much more liable to malarial diseases 
than others ; and voices are often ruined by not breathing 
properly. 

Exercises in SreatJiint/. — The following exercises are re- 
commended to the teacher of elocution, to glA'^e complete con- 
trol of the organs of breathing, and to give elasticity and 
beauty to the voice. They will be found of great advantage 
in giving strength to weak lungs, and vigor and tone to feeble 
voices. 

Full Breathing. — Standing in the proper position, draw in 
the breath slowly until the chest is fully expanded, and then 
emit it with the same degree of slowness. Repeat this as often 
as is convenient. 

Audible Effusive Breathing. — Draw in a full breath as 
before, and expire it audibly in a prolonged sound of the let- 
ter h. It is called effusive, because the breath merely eff\ises 
itself into the surrounding air. It produces a sound some- 
thing like the murmur of a sea-shell. 

Expulsive Breathing. — Draw in a full breath, and then 
9* 



202 METHODS OF TEACUIXG. 

emit it with a strong expulsive force, in the sound of tlie let- 
ter /(, as in a moderate and somewhat prolonged "whispered 
cough." The breath is thus projected into the air. 

Explosive Breathing. — Fill the lungs and then emit the 
breath suddenly and forcibly, in the manner of an abrupt 
" whispered cough." The breath is thus thrown out with 
abrupt force, reminding one of the coughs of a locomotive 
when starting a heav^^ train. 

For an exercise in Sighing, fill the lungs suddenly with a 
full breath and expire it as quickly as possible. For an exer- 
cise in Gasping, inflate the lungs with a convulsive effort, and 
then send forth the breath more gently. For an exercise in 
Panting, breathe quickl}^ and violently, making the emission 
of the breath loud and forcible. 

II. Posture. — Posture has reference to the position of the 
body and its members. The position of a person in reading 
or speaking is a matter that should not be overlooked. A 
person's appearance before an audience has much to do with 
the attention with which people listen to what he saj's. Any- 
thing awkward, clownish, or affected in a person's attitude, 
will naturally prejudice an audience against a reader or 
speaker. 

Elements of Posture Posture includes the position of the 

feet, the hands, the head, and the body. 

The Feet. — The feet should be placed at an angle with each 
other, the weight of the body resting on one foot instead of 
on both. The foot not sustaining the body should be thrown 
slightly forward of the other, in such a position that if drawn 
towards the other, the heel of it would come to the hollow of 
the other. The foot which sustains the weight should be so 
placed that a perpendicular let fall from the pit of the neck 
would pass through its heel, the centre of gravit}^ of the body 
being, for the time, in that line. The sustaining foot is to be 
planted firmly, the leg braced but not contracted, the other 
foot and limb being relaxed and resting for change. The 



I 



TEACHING READING OR ELOCUTION. 2U3 

weight should be occasionally changed from one foot to the 
other, care being taken that the transition be gently and easily 
made. The characteristics of a good attitude are thus firm- 
ness, freedom, simplicity, and grace. 

Another position of the feet is that in which the toes are on 
a line, the feet being slightlj^ inclined to each other, the toes 
turning outward. There are persons with some peculiarity of 
the shape of the legs or feet, to whom this position is more 
suitable than the one previously described. This position is 
usually more becoming to short than to tall persons, and is 
especially suitable to children. 

The errors of position are: continually changing the weight 
of the body from one foot to the other ; swinging to and 
fro ; jerking the body forward at regular intervals, or after 
every emphatic word ; crossing the feet or the legs ; turn- 
ing in the toes ; standing with one foot on a stool or chair 
round, etc. An over-nicety in regard to position that attracts 
attention is also objectionable. Care should be taken to avoid 
all these errors. The posture should be equally removed 
from the awkwardness of the rustic and the afiectation of the 
dancing-master. It should be natural, free from any bad 
habits ; and will thus be both easy and graceful. 

The Hands. — The hands should hang naturally and easily 
down at the side, except when they are being used for ges- 
tures. The fingers should be slightly bent and just touch 
each other, and the thumb should be parallel to the fingers. 
Gentlemen sometimes place one hand at the waist, supported 
by the vest or buttoned coat, and ladies often read and recite 
with one or both hands at the front of the waist. These posi- 
tions are perhaps not very objectionable, but are regarded as 
less elegant than when the hands are at the side. When a 
book is used in reading, it should be generally held in the left 
hand so that the right is free to turn the leaf. 

The errors in the position of the hands are those of place 
and form. The errors of the first class are, — putting the 



204 METHODS OF TEACniNG. 

hands in the pockets, placing them on the hips, playing with 
a button or the watch-guavd, or with any portion of the dress, 
frequent changes as if the person did not know what to do 
with the hands, etc. The errors of the second class are, — ■ 
spreading the fingers, closing the lingers too tightly, sticking 
out the thumb, straightening out the hand, closing the hand 
into a fist, etc. The teacher should carefully note and correct 
all errors, and secure a natural, easy, and graceful position of 
the hands. 

The Head. — The head gives the chief grace to the person, 
and is an important element in delivery. The position of the 
head should be erect and natural. It should not droop, which 
indicates humility or diffidence ; nor be thrown back, which 
indicates arrogance and pride ; nor be inclined to one side, 
which indicates languor, indifference, or clownishness ; nor 
be held too stiff, which indicates a lack of ease and self-pos- 
session. 

The Body. — The position of the body should be erect, easy, 
and natural, with the breast fully fronting the audience. The 
shoulders should be thrown gently back, so as to give the full- 
est freedom and capacity to the organs of the chest. The 
errors to be avoided are, leaning forward or backward, round- 
ing the shoulders, leaning to one side, and being too rigidl}^ 
erect. 

Lanfjuaye of Posture. — There is a natural language in 
posture, a language common to all times and races. The 
movement and position of each member of the body has its 
peculiar significance. 

The Head, held up, denotes pride or courage; hung doicn, 
denotes shame or grief; to nod it foricard implies assent ; to 
tons it back means dissent ; the inclination of the head denotes 
bashfulness or languor; it leans forward in giving attention; 
it is averted in dislike or horror. 

The Ej'es are rained in prayer ; thej^ iceejy in sorrow ; they 
iire cast on vacancy, in tliought ; they are redless, in doubt 



TEACHING READING OR ELOCUTION. 205 

and anxietj'; they stare, in horror and affright ; they look out 
sieaUhili/, iu suspicion or distrust ; they glow, with anger or 
hatred. 

The Anns are projected forward, in authority; they are 
spread extended, in admix'ation ; they are held forward, in 
imploring help ; they fall suddenly, in disappointment ; they 
are folded, in meditation or thoughtfulness. 

The Hand on the head indicates distress or thoughtfulness ; 
on the lips, an inj unction to silence ; on the eyes, shame ; on the 
breast, an appeal to conscience or the affections ; both hands 
nveheld supine or clasped, in prayer; both descend prone, in 
blessing ; they are clasped or wrung, in sorrow and affliction. 
The outstretched hands, with the palms turned away from the 
face, express fear, abhorrence, rejection, or dismissal; with 
the palms toward the face, they denote approval, acceptation, 
welcoming, and love. 

The Body, held erect, indicates steadiness and courage ; 
throivn back, pride; stoojnng forward, condescension or com- 
passion; bending , reverence ov respect; p/-os^ra^ion indicates 
the extremest humility or abasement. 

The Legs, in a firm position, indicate courage or obstinacy; 
bended knees, timidity or weakness, and also reverence; fre- 
quent change, embarrassment or disturbed thoughts ; they 
advance, in desire or courage; they retire, in aversion or fear; 
they start, in terror; they stamp, in authority or anger; they 
kneel, in submission or prayer. 

How Teach, — In teaching posture, the teacher should him- 
self be able to present a model for imitation. He should bo 
careful to correct all errors of feet, body, head, arms, hands, 
etc. He should also make his pupils familiar with the princi- 
ples of posture, as set forth in the language of posture. 

III. Gesture. — By Gesture is meant the movement of the 
body and its members. It is a visible manifestation of thought 
and sentiment which accompanies its oral expression. Gesture 
is one of the most important concomitants of elocution. Some 



206 METHODS OF TEACUING. 

writer remarks, "In the natural order of passionate expres- 
sion, looks are first, gestures second, and words last." De- 
mosthenes, when asked what are the requisites of an orator,- 
replied, " Action, action, action." 

Gesture is the natural language of thought and sentiment. 
It is a universal language, understood by all people. No matter 
what their speech, all know the meaning of gestures, and can 
communicate with one another tliereby. An entire play can 
be presented in pantomime so as to be fully understood. Ges- 
ture is visible language, apparent to the eye as the spoken 
sound is to the ear. When combined with speech, it is thus 
easy to see how it enforces tlie sentiment expressed. Indeed, 
it was a matter of dispute between Roscius and Cicero which 
could produce the greater effect, the former by gesture, or the 
latter by spoken words. 

Gestures may be divided into three classes ; those of Loca- 
tion^ Illustration, and Emphasis. Gestures of Location are 
designed to indicate the position of the object or idea referred 
to. Gestures of Illustration are designed to show the way 
in which something appeared or was affected. Gestures of 
Emphasis are designed to give greater intensity to the mean- 
ing of words or sentences by physical movements. 

Eleuients of Gesture^ — Gesture, in its fullest sense, in- 
cludes the Bow, and the position and movement of the Head, 
the Eyes, the Arms, the Hands, the Body, and the Legs and 
Feet. 

The Bow. — The Brno of a speaker should be graceful, easy, 
and dignified. It should be free from a careless, jerking 
abruptness, and from a formal, unnecessary flourish. It 
should not be too low, so as to seem overdone, nor too short, 
so as to seem trifling or disrespectful. It should not be a 
mere nod of the head, but the entire body should be slightly • 
included in the movement. The body should be bent directl}^ 
forward, and not on one side. The foot ma}- be slightly drawn 
back, or not, as is preferred. Some teachers prefer that there 



TEACHING READING OR ELOCUTION, 207 

shall be a step backward subsequent to the bow; but this is a 
matter of taste, and is not essential. 

• The Hands. — The Hands are the most important members 
in gesture. As Quintilian remarks, these almost speak them- 
selves. "By them we ask, promise, call, dismiss, threaten, 
supplicate, detest, fear; display joy, sorrow, doubt, acknowl- 
edgment, penitence, manner, abundance, number, time." "So 
that amid the great diversity of language among all races and 
nations, this appears to me to be the common speech of all 
men." 

The Form of the hand in making gesture shoxdd be natural 
and unconstrained. The fingers should lie near one another, 
slightly curved, the thumb being parallel with the fingers. 
The gesture with the forefinger is sometimes appropriate, and 
is very expressive when the finger is long and slender. A 
gesture with the fist is very seldom allowable. The errors of 
gesture are, fingers straight and rigid, too much apart, too 
closel}'^ pressed together, thumb projected from the hand, etc. 

The Position of the hand in an ordinary gesture of empha- 
sis, should be a little above the waist, between the waist and 
shoulder. In referring to anything above one, or to grand 
and lofty sentiments, it should be elevated ; in referring to 
anything situated low, or to any low, debased sentiment, etc., 
it should be below the ordinary position. 

The Movements of the baud should be graceful and in good 
taste. The hand should be raised in curved, and not in 
straight lines ; and the movements should also be in gently 
curving lines. Gestures will thus embody the elements oi" 
grace and beautj'. Care should be taken that the movements 
and transitions be not abrupt or angular. After a gesture, 
the hand should fall gently and naturalh' to its place, and not 
go down with a jerk, or with an awkward restraint. 

Tlie Arm. — The Arm, when not used in gesture, should hang 
naturally at the side. In gesture, the elbow should be slightly' 
bent, except in the most emphatic gestures, when it may often 



208 METHODS OF TEACHING. 

be rigid and strai.giit. Care should be taken not to exhibit an 
angle at the elbow. 

The Eyes. — The Eyes, which are an important element of 
expression, should generally be directed as the gesture points, 
except when we wish to condemn, refuse, or require any object 
to be removed. The eye should rest upon the audience, not 
with a familiar stare, but with a kindl3^, modest, and dignified 
expression. To show a modest confidence in your audience 
goes very far to secure their confidence and sympathy. There 
are some motions of the body, legs, and feet which emphasize 
expression, but they need not be discussed here. 

Principles of Gesture. — The primar}' object of gesture is 
to enhance the power of oral language hy the accompaniment 
of visible language. The first principle of gesture is that it 
should be natural and appropriate. The second principle is 
that it should be graceful, moving in fluent and connected 
lines, and not abrupt and desultory. A third principle is that 
strong, bold, determined, and abrupt expressions require 
straight lines ; while all beautiful, graceful, genial, grave, 
grand, and exultant sentiments require curved lines. 

In gestures of location the position of the hand and bod}'" 
should indicate the position of the object referred to. In ges- 
tures of illuatration the physical expression should be appro- 
priate to the thing which is illustrated. In gestures of empha- 
sis the action should fall immediately upon the emphatic word. 

In strong assertion, emphatic declamation, vehement argu- 
ment, or forcible appeal, the descending gesture is to be used. 
In the expression of noble, lofty, and sublime -emotions, the 
ascending gesture is required. In descriptions and all ordi- 
nary sentiment, the middle or horizontal gesture is employed. 

The gesture in front is used in strong and emphatic state- 
ments. The oblique gesture is used in the expression of nega- 
tive sentiments. The extended gesture is used in expressing 
ideas of extent. When the subject is of large extent, the tioo- 
handed gesture is appropriate. 



TEACHING READING OR ELOCUTION, 209 

The hand opened towards the audience indicates kindliness 
of feeling, benevolence, etc. The palm turned away from the 
speaker indicates fear, aversion, etc. Tlie palm turned towards 
the speaker indicates something pertaining to himself. The 
gesture with the closed hand indicates firmness, determina- 
tion, etc. 

We determine the force and extent of the gesture by the 
sentiment expressed. If the sentiment is unemotional, as in 
ordinar}^ conversation, the gestures are moderate, the move- 
ment being mainly from the elbow. If the sentiment is earn- 
est, lofty, and sublime, as in oratory, the gesture is sti'ong and 
wide, the arm moving mainly from the shoulder. If the senti- 
ment is highly impassioned, as in dramatic composition, the 
gestures are still more vigorous and extended. Nice judg- 
ment is required to adapt the gesture to the sentiment, but a 
cultivated taste must be the guide. 

How Teach. — Great care should be taken in teaching ges- 
ture, for it is one of the most important elements of good 
delivery. Gesture is to be taught by Imitation, Principles, 
and Correcting Errors. The teacher should be able to present 
a model in gesture worthy of the imitation of the pupil. He 
should also make the.pupil familiar with the general principles 
which express the natural relation between the sentiment and 
the gesture. He should also be careful to correct all awkward- 
ness of manner, inappropriateness of movement, etc. Some 
of the principal errors are, deficiency of gesture, superfluous 
gesture, random and thoughtless gesture, improper position 
of the hands, improper movement of the arm, awkward replac- 
ing of the hand after a gesture, gesture too early or too late, etc. 

Do not allow pupils to use too many gestures. An excess 
of gesture is like redundancy of language, in bad taste and 
tiresome. Too few gestures are better than too many. Inex- 
pressive or meaningless gestures should be avoided. No ges- 
ture should be made without a reason for it. Some speakers 
accompany nearly every word with a bodily motion, which 



I 



210 METHODS OF TEACHING. 

fatigues the e^-e and offends the taste. A gesture that illus- 
trates nothing is worse than useless ; it destroys the effect at 
which it aims. When a gesture has been assumed, there 
should be no change fi'om it without a reason. The habit of 
allowing the hands to fall to the side immediately after a 
gesture, produces an ungraceful and restless effect. 

IV. Facial Expression. — The face is the mirror of the 
mind. B}'^ nature it reflects promptly all changes of senti- 
ment and feeling. It is therefore one of the most important 
elements of expression. A voice may be artistic in its mod- 
ulations, it ma}'' attune itself harmoniousl}' to language, but 
if the soul of the speaker does not shine out from the coun- 
tenance, much of the power of expression is lost. 
' All the great speakers and writers on oratory have under- 
stood the power of facial expression. Quintilian says, " The 
face is the dominant power of expression. With this we sup- 
plicate; with this we soothe; with this we mourn; with this 
we rejoice; with this we triumph; with this we make our sub- 
missions ; upon this the audience hang ; upon this they keep 
their eyes fixed ; this they examine and study even before a 
word is sijoken." 

Elements of Facial Expression. — The principal features 
in facial expression are the eyes and the mouthy though the 
brow and cheeks aid in expression. 

The Eyes. — The eye is the window of the soul. Out of it 
the soul seems to shine, and the heart can be read b}^ peeping 
in the eyes. "When there is love in the heart," says Beecher, 
" thei-e are rainbows in the e3'es." " The eye," saA's Tucker- 
man, " speaks with an eloquence and truthfulness surpass- 
ing speech. It is the window out of which the winged 
thoughts fly unwittingly. It is the tiny magic mirror on 
whose crystal surface the moods of feeling fitfully' play, like 
the sunlight and shadows on a still stream." Man}' writers 
speak of "the mute eloquence of a look ;" and Byron sings of 
eyes which "looked love to eyes that spake again." 



TEACHING READING OR ELOCUTION; 211 

The Moutli. — The mouth is even more expressive than the 
eyes. The peculiar cliaracter of the face is largely due to the 
size and shape of the mouth. A small mouth indicates 
secretiveness ; a large mouth, open-heartedness and good 
humor ; parted lips indicate listlessness or stupidity ; com- 
pressed lips are a sign of firmness and decision of character ; etc. 

The expression of the mouth is due principally to the 
coruers of the mouth. We draw up the corners of the mouth 
iu laughing, and depress them in cr3'ing. " To be down in 
the mouth" is an expressive phrase for low spirits. In a 
picture the same face may be changed from laughter to weep- 
ing by merely making a cliange in the corners of the mouth. 

How Teach. — In facial expression nature must be our 
guide. The soul must feel the sentiment to be expressed, and 
the countenance must be the mirror of the soul. The pla}^ of 
features must respond to the sentiment stirring in the heart. 
The following propositions will indicate the general principles 
of facial expression. 

Unemotional sentiments require the countenance to be in 
repose. Sentiments of good humor, happiness, etc., require a 
pleasant and smiling countenance. Bold, grand, and noble 
sentiments require dignity and animation of countenance. 
Humorous sentiments require the play of humor in the face ; 
sad and pathetic sentiment should be accompanied with a 
dejected and softened expression ; shame requires the averted 
e^^es and blush of guilt. Determination, anger, and a spirit 
of defiance are expressed by a contracted brow and com- 
pressed lips ; in scorn we elevate the upper lip and nose ; in 
fear, surprise, and secresy, the brow is raised, the eyes are 
opened, and the lips parted. 

General Sug-gestions. — We close this chapter on Reading 
witli two or three philosophical suggestions of practical value. 
The question is often asked, What is the standard of cul- 
ture in Reading, and by what standard shall we judge the 
reading of an Elocutionist? 



212 METHODS OF TEACHING. 

Reading is an Art, and tlae basis of all Art is Natiu'e. The 
basis of all good expression is therefore natural expression. 
But what is natural expression? Not every one's manner of 
reading before any culture in the art, can be called natural 
reading. Our powers have become so enfeebled and modified 
by fashion and habit as to have departed from nature. Indeed, 
man acquires so many artificial habits that he often finds it 
one of the most natural things to be unnatural. We must 
therefore be careful not to confound habit with nature. We 
say it is natural for some persons to talk through the nose ; 
but this is habit rather than nature. True ai't leads to nature 
and not to the artificial forms of habit. Nature is alwa^'S 
pure, true, and beautiful. Culture endeavors to discover what 
is natural, and to take each individual back to that high 
standard from which he has departed. 

The object of culture in Elocution is therefore natural ex- 
pression. It aims not to eliminate, but to train and improve 
the natural expression. Everj^thing artificial in expression 
is regarded as inartistic and distasteful. The reader who 
" shows his elocution" in his reading offends good taste, and 
shows his shallowness of mind and the imperfection of his art. 
In elocution especially, we should endeavor to attain that 
excellent standard of culture in which " the highest art con- 
ceals art." 

This culture must be on the basis of our own individual 
nature. We cannot substitute some one else for ourselves 
without incongruity, any more than we can wear one another's 
clothes without a sense of unfitness, Cultui'e seeks to find 
out and develop our own natural powers, rather than to 
attempt to substitute others for them. Tlie character of our 
expression must be in harmony with our own individual 
nature. Elocution has often been made ridiculous by tlie 
incongruous attempts of one reader to adopt the style and 
manner of another. 

We are to look for natiU'e in conversation. Natural, re- 



TEACHING READING OK ELOCUTION, 213 

fined, and cnltivated conversation is the basis of the art of 
Elocution. Conversation is the simplest and most common 
form of human expression. "It contains the germs of all 
speech and action,''^ and thus constitutes the basis of all cor- 
rect deliveiy. The importance of cultivating correct habits 
of voice and manner in conversation cannot be over-estimated. 
Conversation is a beautiful art, and deserves culture for its 
own sake, and also as a basis of elocutionarj' cultui'e. 

The standard by which we judge of good reading is a cul- 
tivated taste. Man has been endowed with an a3sthetic 
nature, which when properly cultivated b}^ the influence of 
natural expression in art, enables him to sit in criticism upon 
the productions of the artist. Where, through personal 
idiosyncrasies, tastes seem to differ, we are to be controlled in 
our decision by the opinions of the majority of cultivated 
persons. 

In conclusion, we urge teachers to remember that elocution 
is a beautiful art and worthy of the highest culture. Yoice 
and speech are divine gifts, and should be trained to their 
highest excellence. As Prof. Shoemaker so well remarks, 
" It is only the voice that has reached its best, and the eye 
that beams from the soul, and the hand of grace, and the atti- 
tude of manhood and womanhood, that can convey the immor- 
tality that has been breathed upon us." As God manifests 
His glorious attributes in the expression of Nature and the 
Bible, and above all in the Eternal Word, so may we show 
the image of divinity in our souls by a pure, natural, beauti- 
ful, and artistic expression. 



CHAPTER Vn. 



TEACHING LEXICOLOGY. 



LEXICOLOGY treats of the meaning gf words. The term 
is derived from lexicon, a dictionary, and logos, a dis- 
course. It is usually employed to embrace the origin and 
significance of words ; but it is here used as relating onl}^ to 
the meaning and proper use of words. 

The meaning of words is largely taught in all the branches 
of language. The subject, consequently, does not need a 
lengthy treatment by itself. No formal study of the subject 
is suggested for the ordinary common school; but much can 
be done in all the studies to lead pupils to notice new words, 
learn their meaning, and fix them in their memory. In the 
higher classes, oral lessons might be given on the subject ; and 
in advanced schools there should be a regular course of study 
to teach the meaning and use of words. A few suggestions 
will be made to guide the teacher in his work. 

Bi/ their Use — The meaning of words is taught b}' their 
use in conversation and speaking. The child first learns the 
meaning of words from the mother and father and other mem- 
bers of the household. The words he uses have never been 
explained to him; no definitions have been given him ; but he 
uses them correctl}^ because he has heard them so used. Usage 
is his guide in using language. If he has been accustomed to 
hearing a correct and refined vocabulary, he will express 
himself with correctness and refinement. It is of inestimable 
advantage in linguistic culture to listen to the conversation 
of intelligent ami cultivated people. It is said that the 
Gracchi obtained the elegant use of language from their 
accomplished mother Cornelia ; and Aristotle imbibed from 

(214) 



TEACHIXQ LEXICOLOGY. 215 

his mother " that pure and sweet Atticism which everywhere 
pervades his writings." 

JBy Reading. — The meaning of words is learned from read- 
ing. This is one of the most practical ways in which such a 
knowledge is acquired. In literature we see the correct use 
of the word, which we cannot alwaj^s tell from the definition. 
We also learn to appreciate those nice shades of meaning 
which cannot be stated in a definition. Pupils who read most 
haA- e usually the largest vocabulary and the best use of words. 
Young children will often be heard using the words in their 
conversation which they have met with in some book recently 
read; and, if properl}'- taught, their compositions will show 
the same thing. Children should therefore be encouraged to 
read extensiveh'' and to read the best written works. 

Teachers should call attention to the meaning and use of 
words in the reading lesson. They should require pupils to 
put the unusual and difficult words into sentences to see that 
they know how to use them. In this way the word is fixed 
in the memor}', and the child's vocabulary enlarged. The 
reading class presents one of the very best opportunities for 
teaching the meaning of words. 

Sy Illustrations. — With young pupils, the meaning of 
words may be taught bi/ means of objects or illastrations. 
Thus, the meaning of the word transparent may be illustrated 
with a piece of clear glass ; the meaning of the word translu- 
cent, by a piece of ground or painted glass ; the word opaque^ 
by any object which does not permit the light to pass through 
it. The best way to teach the meaning of a bone is to show 
the pupils a bone; and the same may be said of calyx, corolla, 
stamen, pistil, etc. Most of the terms of the natural sciences 
may be taught in this way, and many of those in the abstract 
sciences, as the names of the figures in geometry. Object 
Lessons are especially valuable in this respect. 

By Definitions. — The meaning of words maj^ be taught l)y 
means of popular definitions. The unknown word ma}' be 



2 If) METHODS OF TEACHING. 

made known by comparing it with one alread}' understood, or 
b}' the use of several words which explain it. Care should he 
taken, however, that the term used in the definition is simpler 
or better known than the word defined. This is not always the 
case with the definitions given in onr text-books, especially 
those found in some of our school readers. To define shorten 
as abbreviate, or correct as rectify, or buying as purchasing, or 
belong as a])pertain, etc., gives the pupil another word for the 
same idea, but does not give him any new idea of the first 
word. 

The Dictionary/. — The meaning of words can be taught by 
a careful use of the dictionary. Pupils, as soon as they are 
old enough, should be required to make frequent use of the 
dictionar}^ This should become a habit with them. The 
great masters of language made the dictionar}^ their constant 
companion. Rnfus Choate, so eminent by his scholarly use 
of the English language, was a constant and thorough student 
of the dictionarj^ 

In the stud3' of definitions, it should be remembered that 
we cannot always know how to use a word from its definition. 
Thus abandon means to forsake, to gice up, etc.; but it would 
not be correct to say we "forsake a study" or cA^en "abandon 
a bad habit," etc. Abbreviate means to shorten, but we would 
not appropriately speak of abbreviating a dress or a string or 
a stick of timber. We must notice the use of words in sen- 
tences in order to understand the nice distinctions between 
them ; and definitions should always be accompanied by sen- 
tences illustrating the proper use of the term defined. 

A pupil should acquire the habit of marking down every 
new word which he meets, or every word which he thinks is 
not a part of his practical vocabulary. He should keep a list 
of such words, frequently refer to them, and make use of them 
in speaking and writing. He will thus enlarge his stock of 
words, and learn to use them with readiness and precision of 
raeaninof. 



I 



TEACHING LEXICOLOGY. 217 

From Synonyms. — The meaning of words may be taught 
by the study of aynonyms. By synonj^ms we mean words of 
the same general significance, yet with slight shades of differ- 
ence in their meaning. They are words which, with great and 
essential resemblances of meaning, have, at the same time, 
small, subordinate, and partial differences. These differences 
may have originally inhered in them, or they may have ac- 
quired them by general usage, or some earlj^ and latent mean- 
ing may have been awakened by the special usage of some 
"wise and discreet master of the tongue." 

The English language is especially rich in synonyms. This 
arises from its being a composite language, words for the same 
thing being derived from different sources. Many of these 
in time became differentiated and now constitute our syno- 
nyms. Thus motherly and maternal, fatherly and p'^ternal, 
happiness and felicity, daily and diurnal, poicerful and poten- 
tial, etc., are pairs of words meaning very nearly the same, 
the first in each case coming from the Anglo-Saxon and the 
second from the Latin. 

The study of S3^non3'^ms is especiall}'^ valuable in learning to 
use words correctly. It enables the pupil to see those nicer 
and more delicate shades of meaning by which words are dis- 
tinguished. It enables them to see in what cases words may 
be used interchangeably, and where they cannot be; thus we 
ma}^ Bay force of mind or strength of mind, but not strength 
of gravitation. It is only by a careful comparison of words 
that a pupil can use such words as the following correctl}': 
invent -awd discover ; only and alone ; enough and sufficient , 
avow, acknowledge, and confess; hill, murder, and assassinate 
Crabb's Dictionary of Synonyms is an excellent work for 
such a study, though the subject is quite fully presented in 
Webster's and Worcester's large dictionaries. 

Logical Definitions. — The meaning of words maybe taught 
by means of logical definitions. A logical definition is one 
which defines by means of the class and specific difference, 
r » 



218 METHODS OF TEACHING. 

called genus and differentia. Thus, a triangle is a polygon of 
three sides and three angles. Here polygon is the genus, and 
three-sicltedness the specific difference. The practice of study- 
ing logical definitions tends to sharpen our conceptions of 
the distinction of words, and to cultivate the habit of careful 
discrimination in the use of language. 

Many terms will not admit of a logical definition. Such a 
definition is only possible when the genus and specific differ- 
ence can both be stated. Terms expressing simple ideas can- 
not be logically defined, because they cannot be resolved into 
their elements, and are thus without genus and differentia. 
Thus, truth, sjMce, being, etc., will not admit of a logical defi- 
nition. Some terms, though belonging to a genus, cannot be 
defined on account of our being unable to state the differentia. 
Thus, in the statement red is a color, color is the genus, but 
who can give the differentia, the difference that separates red 
from the other colors? 

Ltitin and GrceJx. — The meaning of words may be learned 
by the study of Latin and Greek. The practice of looking in 
the dictionary to find the English words which correspond to 
the words in other languages, makes the pupil familiar with 
the meaning and use of the English words. The constant use 
and comparison of words, necessary in translation, gives 
linguistic accuracy and a facility in their use. The process 
of translating cultivates that fine literary sense by which the 
delicate shades of meaning among words are perceived and 
appreciated. 

From Effjniolof/y — The meaning of words may be taught 
by the study of Etymology. A knowledge of the origin of a 
word sometimes aids us in understanding its meaning and use. 
Thus it adds to our idea of the word Education to know that 
it means to draw out, e and duco, and also subtraction, to 
know that it means to draw from under, sub and traho. The 
etymology often enriches and enlarges the meaning of a 
word, and puts an expressiveness in it by the image it brings 
before the mind as we use it. 



TEACHING LEXICOLOGY. 219 

"We cannot always use a word correctly, however, by know- 
ing its etymology. Indeed, the etymology of a word would 
usually lead us astray in its use. Thus the word subtraction, 
even, could not be used in its literal etymological sense of 
clraxoing frovi under. The same may be said of Tight, wrong, 
conduct, normal, and a multiplicit}^ of words which could be 
named. The principal use of etymology, aside from the inter- 
est and intrinsic value of the knowledge, is that it puts into 
the mind a concrete image which seems to add force or empha- 
sis to its meaning. 

There are two methods of teaching etymology; the Ana- 
lytic Method and the Synthetic Method. The Analytic Method 
begins with the word as a whole and separates it into its Qiy- 
mological parts, showing the meaning of the parts, and thus 
the meaning of their synthesis in the word. Thus, after the 
child is familiar with the word subtraction, it may be shown 
that it consists of the three parts, sub meaining under, tract 
from traho, I draw, and ion, the act of. A large number of 
words may be analyzed in this way as they occur, and a 
knowledge of the elements be reached through the words. 

The Synthetic Method begins by teaching a list of prefixes 
and suffixes and roots, and then unites them in forming- 
words. Thus, after committing elements, the pupil may be 
shown that sub and tract, a modification of traho, and ion, 
give the word subtraction. In actual practice, there is a sort 
of aualj^sis of each word into the elements which have been 
previously learned ; but the spirit of the process is synthetic, 
since it passes from the elements to the word containing 
them. 

Of these two methods, the analytic is the better for begin- 
ners. It is the more interesting method ; the committing 
of a list of roots is rather dry work. It is also in accordance 
with the law of instruction, from the known to the unknown; 
while the synthetic method inverts this law. It also begins 
in the concrete, while the other is abstract. For advanced 



220 METHODS OF TEACHING. 

pupils the .S3'ntheti(; method ma}'^ be preferred, as it is more 
formal and thorough in its procedure. 

Teachers should take pains to call the attention of pupils 
to the etymology of words. Even some incidental instruction 
of this kind will give the pupil a knowledge of the elements 
of a large number of words; and, what is better, cultivate a 
taste for etymology. They should not restrict their instruc- 
tion to Latin and Greek elements, but should call attention 
to the Saxon elements also. Such words as England^ wife^ 
husband, knave, heathen, etc., will be full of interest to chil- 
dren. Every teacher sliould have a copy of "Trench on the 
Study of Words," and besides this it would be well for them 
to read Max Muller, Whitney, Scheie de Vere, etc. 



CnAPTER VITL 

TEACHING ENGLISH GRAMMAR. 

GRAMMAR is the science of sentences, English Grammar 
is the science of the English sentence. It treats of the 
relation and construction of words in sentences. In other 
words, grammar is the science of the sentential use of words, 
Tiie term (jrammar seems to have been derived from gravima, 
a letter, which came from grapho, I write. 

Grammar has sometimes 1)een defined as "the science of 
language." This definition includes too much, for there 
are several other l)ranchcs of language coordinate with gram- 
mar, as Rhetoric, Etymology, Pliilology, etc. It is sometimes 
defined as " the science wliich teaches us to speak and write 
the English language correctly;" but this also includes too 
mucli, as other branches aim at the same result. A sentence 
may l)e grammatically correct and still be incorrect in regard 
to other departments of language. Besides, it is not proper 
to define a science as " that which teaches" something. 

There is so close a relation between grammar and the two 
branches, Rlictoric and Logic, that it is difTlcult to state 
clearly the distinction between them. Logic is the science of 
thought; but since this thought must be expressed, Logic 
deals also to some extent with the expression of thought. 
Rhetoric also treats of the manner in wliich thought and senti- 
ment are expressed. Popularly we may say, — Logic teaches 
clearness of expression ; Grammar, correctness of expression ; 
and Rhetoric, effectiveness of expression. Fowler, in tittempt- 
ing to distinguish these three branches, says : " Logic deals 
with the meaninrj of language; Grammar with its construction ; 
and Rhetoric with its persuasiveness. Logic plans the tern- 

(221) 



222 METHODS OF TEACHING. 

pie; Grammar builds it: Rhetoric adorns it." It is clear that 
since thought determines expression, the science of logic is 
very intimately related to a full understanding of the subject 
of Grammar. 

The term Grammar was formerly used in a broader sense 
than at the present day. In its widest acceptation, and this 
was its primary use, it included all verbal expression of the 
products of the mind. Trench says, "Grammar is the logic 
of speech, even as Logic is the grammar of reason." It has 
also been used to signify a treatise on the elements or princi- 
ples of any science; as, a "gi-ammar of geography," a "gram- 
mar of arithmetic." The term has, however, become differ- 
entiated so as to be now restricted to the sentential use of 
words. 

I. General Nature of the Subject. 

I. Nature of Grammar.^ — To aid the student in understand- 
ing the methods of teaching grammar, we shall present a brief 
statement of the nature of the science. A conception of the 
subject of grammar may be presented in two Avays ; first, by 
considering the office of the individual words in a sentence ; 
and second, by resolving the sentence into the thought 
elements which enter into its structure. The former is called 
the Etymological view of grammar ; the latter is called the 
Logical view of the subject. 

Etyinolofjical Elements. — Language is made up of indi- 
vidual words. These words are all embraced under a few 
general classes, some eight or ten, called Parts of Speech. 
Each one of these parts of speech performs a certain office in 
a sentence, and some perform two or three offices. 

Parts of Speech. — The first and simplest class of words are 
those Avhich are the names of objects, called Nouns. There 
are also words expi'essing some action or state of the objects 
named by these nouns, which are called Vei-hs. Then there is 
a class of words, usually expressing qualities, which are added 



TEACHING ENGLISH GRAMMAR 223 

to the nouns to distinguish the objects referred to b}' the 
noun ; these are called Adjectives. Then we have a class of 
words used to distinguish the actions expressed b}' the verbs, 
called Adverbs. The words used to distinguish the qualities 
expressed by adjectives and by adverbs are also called adverbs. 

Then there is a class of words used for nouns, called P7'0- 
nouns. There is also a class of words used to connect other 
words and show the relation between them, called Preposi- 
tions. We have also words which connect words and sen- 
tences without showing any relation between the words 
connected, which are called Conjunctions. There are words 
also which express feelings or emotions, which on account of 
their being thrown into the sentences formed by other words, 
are called Interjections. 

Properties of Parts of Speech. — These parts of speech have 
certain relations to one another and to the things which they 
express, that give rise to certain changes in their form or 
meaning. These changes in form are called Inflections, from 
flecto, I bend, since the form of the word is changed, as in 
bending an object we change its form. Words w'hich admit 
of such changes are said to be declinable, from de, down, and 
clino, I lean or incline. In many cases in the English lan- 
guage there is no change of form to indicate the relation, 
though the relation realh^ exists, and is thought if it cannot 
be seen. These are all embraced under the head of the Prop- 
erties of the parts of speech. 

The properties of the Noun are Nuviber, Person, Gender, 
and Case. The properties of the Verb are Mode, Tense, and 
Voice, and also Person and Number derived from its subject. 
The change in the adjective and adverb is called Comparison. 
In some languages the adjective has the properties of number 
and case, which it seems to have derived from the noun. 

Classes of Parts of Sjjeech — These Parts of Speech admit 
of various divisions into classes, which give us what are called 
the Classes of the Parts of Speech. Thus, Nouns are divided 



22-1: METHODS OF TEACHING. 

into Proper and Common^ etc.; Verbs into Regular and Irreg- 
tilar, Transitive and Intransitive, etc.; Pronouns into Per- 
sonal, Relative, Interrogative, etc.; Conjunctions into Coor- 
dinate and Subordinate ; etc. 

Rules of Construction. — From the consideration of the rela- 
tion of these words to one another, and a careful examination 
of the usage of cultivated men and women, we derive certain 
laws of construction, which constitute the Rules of Grammar. 

Some Terms. — Then we have certain offices ascribed to the 
words as limit, modify, govern, etc. One word is said to 
limit another when it limits its application to a part of the 
■class of objects which it represents; thus, in the expression 
blue birds, the word blue limits the word birds to only a part 
of the general class of birds. The term modify means very 
nearly the same as limit, one word modifying the application 
of another word ; as in red roses, the red modifies the applica- 
tion of the word roses. By government in grammar is meant 
the power that one word is supposed to exercise over another 
word to cause it to assume some particular form or meaning. 

Logical Elements. — In this statement we have a brief out- 
line of the nature of grammar, derived from the consideration of 
the individual words in a sentence. There is another method 
of conceiving the subject, however, which consists in deter- 
mining the elements of language by regaixling the sentence as 
a unit, and analyzing it into the necessary parts of which it 
is comjiosed. We state briefly the results of such an analysis. 

Principal Elements. — A sentence is an assertion of some- 
thing about something. Every sentence thus contains two 
necessary elements ; that about which an assertion is made, 
and that which is asserted. These two elements are distin- 
guished as the Subject and the Predicate. The Subject may 
consist of a single loord, or of a collection of words not form- 
ing a proposition, called a phrase, or of a collection of words 
containing a proposition, called a clause. Similarly, the Pred- 
icate ma}'' consist of a word, a phrase, or a clause. 



TEACHING ENGLISH GRAMMAR. 225 

Subordinate Elements. — Continuing the analysis, we find 
that some elements are used to limit, modify, or describe 
other elements, and these we call modifying or liniiting ele- 
ments. When they limit the meaning or application of words 
used as the names of objects, they are called adjective ele- 
ments; when they limit the meaning or application of words 
used to express actions or qualities, they are called adverbial 
elements. These elements are often called adjuncts^ because 
they are joined to the elements which they limit. To distin- 
guish them from the subject and predicate, they arc called 
subordinate elements^ the subject and predicate being called 
principal elements. These suboi'dinate elements are, with 
respect to their form, of three classes; words^ phrases^ and 
clauses; and with respect to their use the}^ are also of three 
classes; adjective, adverbial, and objective. 

Connective Elements. — In addition to the principal and sub- 
ordinate elements, there are also words used to connect the 
other elements, which are called connective elements. We 
also often find in language words that have no logical connec- 
tion with the other words ; such words are called independent 
elements. 

This method of looking at a sentence and reaching its ele- 
ments may be called the logical method, in distinction from 
the other method, which may be called the etymological method. 
There is another method presented by Prof. Welch in his 
work entitled " The Analysis of the Sentence," which seems 
to combine both of these methods. This method we will also 
state. 

Mixed Method. — All language is made up of three classes 
of elements ; words, phrases, and clauses. The Word is the 
simplest grammatical element, and performs nine oflSees: 
1. The subject of a sentence; 2. A verb; 3. An object of a 
transitive verb ; 4. Complement of a neuter verb; 5. Essential 
Element of a Phrase; 6. Adnorainal Word; 1. Adverbial 
Word ; 8. Connective ; 9. Independent Word. 
10* 



226 METHODS OF TEACHIXG. 

A Phrase is an element composed of a noun or pronoun and 
its connective, generall}^ used to limit a word. Phrases are of 
two kinds; adnominal and adverbial, according as they limit 
like an adjective or an adverb. The Sentence is a group of 
elements expressing a thought. Sentences are of three 
classes; transitive, intransitive, and neuter. They are also 
independent and dependent. An independent sentence is one 
that makes complete sense in itself; a dependent sentence is 
one that does not make complete sense in itself. Dependent 
sentences are nominal, adnominal, or adverbial, according ?is 
they fulfill the office of a noun, an adjective, or an adverb. 
Connectives are either coordinate or subordinate, or second- 
ary, each of which has a distinct office in the construction 
of sentences. 

It is noticed tha't this analysis of the elements of sentences 
makes use of logical ideas, and that the office and names of 
the elements ai-e determined by the etymological use of words. 
In other words, this " Analysis of the Sentence" though some- 
what logical, is dependent on a knowledge of the etymological 
use of words in a sentence. Some authors present a logical 
analysis a little different from either of these, but involving 
the same general principles. Nearly all depend more or less 
upon a knowledge of etymological grammar in naming and 
defining the logical elements. 

II. Origin of Grammatical Elements. — Having pointed out 
the grammatical elements of language, the questions naturally 
arise, — How did these elements originate? Why have we just 
so many parts of speech ; and wh}' are they such as they are? 
We shall endeavor to give a brief repl}^ to these questions. 
There are two theories upon this subject; one drawn from the 
consideration of the operation of the several faculties of the 
mind, and the other that presented b^'^ the writers on logic. 
These two views, for want of better names, we may distinguish 
as a New and the Old theory. 

A New Theory. — Language is the product of the human 



TEACHING ENGLISH GRAMMAil 227 

mind. The thought went out into expression, and thus gave 
form to the language. In order, therefore, to understand the 
growth and nature of the grammar of the language, we must 
look at it through the laws of mental activity. 

Parts of Speech. — The faculty of the mind which first 
awakens into activity is Perception. Perception cognizes 
individual things, and forms particula?^ ideas. These ideas 
we express in particular words; hence our first words are 
names which we call nouns^ from nomen, a name. These names 
are of individuals and are thus jyroper nouns, or have the 
'force of proper nouns. The mind also sees these objects ac^- 
ing or doing something, which it expresses in the form of 
action or doing words. These words are called verbs, from 
verhum, a word, because they are regarded as the most import- 
ant words in a sentence. These verbs, like the nouns, at first 
express particular actions. 

The mind, at first, cognizes objects as wholes, without dis- 
tinctly noticing their attributes ; but it soon begins to analyze 
them and to distinguish their qualities ; the naming of these 
qualities in their relation to the objects, gives us words to 
distinguish objects, which on account of their being added to 
nouns, we may call adnouns; or, since they are thrown to 
nouns, they have been called adjectives, from ad, to, and Jacio, 
I throw. The mind also compares actions and notices their 
differences ; the naming of these differences in relation to the 
action, gives us a class of words to distinguish actions; which, 
on account of their being added to verbs, are appropriately 
called adverbs. 

The mind in comparing objects, notices these similarities, 
and brings the similar objects together under a common name; 
it thus forms general ideas which give rise to general terms or 
common nouns. In a similar manner, the verb, which was at 
first the name of some particular action, becomes general in its 
application to a class of similar actions. The adjective and the 
adverb also become more general as our experience enlarges. 



228 METUODS OF TEACHING. 

Having obtained general notions, the mind begins to com- 
pai"C these general notions, and perceiving a relation between 
them, forms judgments, wliicla when expressed, give us the 
proposition. Tliese judgments or propositions need a connect- 
ing or aflirming word, which gives rise to the copulaov neuter 
verb as " man is an animal." The affirmation of an attribute 
of a general notion (regarding the intension of the concept) 
also requires the use of the copula, as " man is mortal." 

As our progress in thought and language continues, it is 
found convenient to avoid the too frequent repetition of nouns, 
wliich we do by the introduction of a class of words to be 
used for nouns^ which we call for-noiuis, or pronouns. If it 
were necessary to have a class of words to avoid the too fre- 
quent repetition of the verb, we sliould have a class of far- 
verbs or pro-verbs also, which we seem to approximate in the 
peculiar use of the word do; as "John studies, and so do I." 

In order to unite and show the relation of some of the 
words we use in tlie construction of sentences, it was neces- 
sary to introduce words expressing relations, which we may 
call relation-words; or, since they are placed before the word 
to be related to some other word, they are called prepositions^ 
from prae, before, and pono^ I place. Words used merely to 
conjoin words and sentences Avere also necessar}'-, and were 
called conjoining ivords, or conjunctions. Words expressing 
emotions were also needed, and since these words had no 
relation to the rest of the sentence, but were thrown in 
abruptly between other words, the}' were called interjections, 
from inter, between, and Jacio, I throw. 

The Properties. — We may also account for the origin of the 
inflections, or properties of the parts of speech in a similar 
manner. It was necessar^^ to distinguish between the use of a 
noun as meaning one or more than one object, and this was con- 
veniently done by a change of termination in the nouns to in- 
dicate this meaning, which gave rise to the property o( number. 
For all practical purposes two forms were sufficient ; hence 



TEACHIXG ENGLISH GRAMMAR. 229 

we have only two numbers, lingular and iDlural. Some 
nations, however, seemed to find it convenient to distinguisli 
between one, two, and more than two things ; and thus iirose 
a third form, called the dual nuTnber. This dual form is sup- 
posed to have been caused by the duality of the parts of the 
human body, as the eyes, the hands, etc. 

Since there were two objects of the same class of animals 
distinguished by sex, it is natural that words should be 
changed in their form to distinguish the sex of the object 
named ; and thus arose the property of gender. Since a noun 
could represent the three persons, the speaker, the person 
spoken to, and the person spoken of, there naturally arose a 
change of form in the noun to indicate the person ; which gave 
rise to the property, called the person of nouns. The differ- 
ent relations that an object may sustain to an action or to 
another object, caused a change of termination to indicate the 
relation meant ; and this gave the property of case^ six in 
Latin and eight in Sanskrit. In our language these relations 
are principally expressed by prepositions, leaving us only 
three cases for pronouns, and, some say, only two cases for 
nouns, the nominative and the possessive. All these proper- 
ties of nouns would, of course, belong to pronouns as their 
representatives. 

The properties of the verb originated in a similar manner. 
The fact that a verb could be used in commanding, or inquir- 
ing, or simply declaring an action, gave rise to the property 
of the manner or mode of the verb. The idea of time and the 
fact that the action expressed by a verb could take place in 
ditferent times, gave rise to a change of the verb to indicate 
these times of an action, which produced the property of tense. 
It was natural for the form of the verb to vary as the number 
and person of its subject varied, and r,his gave rise to the 
number i\.\\(\. person of the verb. 

The number and person of a verb are not intrinsic, but deriv- 
ative properties of the verb ; and by some grammarians are 



230 METHODS OF TEACHING. 

not regarded as properties at all. A certain writer saj-s that 
to attribute person and number to a verb is "as anomalous as 
to assign gender and number to adjectives. Most languages 
fall into this error, which is, however, susceptible of a very 
easy historical solution. It arose, doubtless, from the original 
custom of annexing the pronoun to the termination of the 
verb, and continuing the use of the inflection after its import 
had been forgotten, and when the pronoun had been formed 
into an independent part of speech." 

It seems to have been natural, primaril}', to express the 
relation of words by an affix or prefix to the radical portion 
of the word ; these changes seem subsequently to have been 
replaced by particles. The earlier stage of a language is usu- 
ally richer in terminations ; which drop off as the faculty of 
abstraction becomes habitual. In a manner similar to that 
now explained, we can account for every grammatical distinc- 
tion b3' a development from the natural psychological opera- 
tions which give form to language. The different Classes of 
parts of speech arise from the different offices performed by 
words of the same general class, and the Rules of Construc- 
tion grew out of the laws impressed upon language by thought, 
modified by the circumstances of fashion, etc., which intro- 
duced changes into the language of the people. 

The Old Theory. — We have thus indicated what we con- 
ceive to be a correct idea of the development of grammatical 
elements from the natural operation of the human mind. 
There is, however, another view of the subject, drawn from 
logic rather than from psycholog}'. We will briefl}' indicate 
this view. 

It is held that the first class of words are substantives, so 
called because they are conceived as standing under (siib- 
stayis) certain qualities. These qualities may also be consid- 
ered as substantives, as whiteness, greenness; but when con- 
sidered in relation to the substances of which they are proper- 
ties, they constitute a second class of words, adjectives or 



TEACHING ENGLISH GRAMMAR. 231 

noun-adjectives. A conception^ or general notion, when 
formed, is capable of being resolved back into its constituent 
parts or qualities ; and the attribution of a qualit}'^ to a sub- 
stance leads to a judgment ; as "Snow is white," the sign of 
the attribution being called the copula. When the quality 
is combined with the copula, a third class of words is pro- 
duced, which we call vej^bs. Thus, instead of saying, "the 
sun is bright," we may say " the sun shines." A verb is 
thus regarded as a compound part of speech, consisting of 
an adjective and a copula or affirmation. These three parts 
of speech — the substantive^ the adjective^ and the verh^ are 
called the primary or essential parts of speech. 

The adverb, it is said, derives its existence from the difficulty 
of defining by one word the precise quality of a particular 
object. Words are needed to indicate the degree of the quality 
expressed. The primary use of the adverb, it is thus seen, is 
to modify the quality or attribute expi-essed by the adjective 
and the verb. Prepositions are said to express relations be- 
tween substances, objective relations; while conjunctions may 
be regarded as expressing subjective relations, or those exist- 
ing between judgments, whether of mere succession, of infer- 
ence, or the like. The other grammatical elements would be 
derived very nearly in the manner previously explained. 

III. Origin of Grammar. — Grammar originated among the 
Greelcs. It seems to have had its origin about the second 
century B. C, among the scholars of Alexandria. Many of 
them were engaged in preparing correct texts of the Greek 
classics, esi>ecialh^ of Homer. The manuscripts differed, and 
the correct form was determined by a comparison with the 
language of Homer. They were thus forced to pay attention 
to grammatical structure, and to observe the laws of con- 
struction. The first real Greek grammar was that of Diou}^- 
sius Thrax, a pupil of Aristarchus. He went to Rome as a 
teacher about the time of Pompey, and wrote a practical 
grammar, it is supposed, for the use of his pupils. This work 



282 METHODS OF TEACHING. 

was the foundation of grammar. Later writers have improved 
and completed it, but have added nothing really new and 
original in principle. 

The earliest scientific investigations of language among the 
Greeks were not strictly grammatical, but discussed the rela- 
tion of thought to expression. The distinction of subject and 
predicate, and even the technical terms of case, number, and 
gender, were first used to express the nature of thought, and 
not the forms of language. The early Greeks had a ver}^ slight 
knowledge of grammar proper. Plato knew the noun and 
verb, as two component parts of speech. Aristotle added con- 
junctions and articles, and observed the distinctions of num- 
ber and case. The word article with him, however, meant a 
socket in which the members of the sentence moved, and in- 
cluded many more words than at present. Before Zenodotus, 
250 B. C, all pronouns were simply classed as sockets or arti- 
cles of speech. He was the first to introduce a distinction 
between personal pronouns and mere articles or articulations 
of speech. Aristotle had no technical terms, as singular or 
jilural, and does not allude to the dual. Zenodotus seems to 
have been the first to observe the use of the dual in the 
Homeric poems, and changed many plurals into duals. 

The first attempt at an English grammar was PauVs Acci- 
dence, an English introduction to Lill3''s Latin grammar, 
written by Dr. John Colet in 1510. Lill3''s grammar received 
the sanction of roj'al authority and was the exclusive stand- 
ard in England for more than 300 years. The first book 
treating exclusively of English grammar was written by Wil- 
liam Bullokar in 1586. During the next century, several works 
on grammar were written, among which are mentioned one by 
Ben Jonson (1634), one b}^ Dr. John Wallis (1653) in Latin, 
and one by William Walker (1684), the preceptor of Sir Isaac 
Newton, also in Latin. In 1758, Bishop Lowth published his 
celebrated grammar, an excellent work from which Lindley 
Murray drew most of his materials. Lindley Murray published 



TEACHING ENGLISH GRAMMAR. 233 

his first grammar in 1795, and his Abridgement in 1197, a 
work' which has been extensivel}'^ used in this country and in 
England. The annual sale of the book in England has been 
estimated at 50,000 copies. This popular work was largely 
derived from Lowth and Priestley, and owed its popularity 
to its practical adaptation to tire work of the school-room. 
The number of grammars published in this country is legion ; 
the ablest and most celebrated is that of Goold Brown. The 
first to develop and give prominence to "grammatical analy- 
sis," was Prof. S. S. Grreene, of Brown University. 

IV. The Teaching of Grammar. — Having spoken of the 
nature of grammar, the origin of the grammatical elements, 
and the historical development of the subject, we shall now 
call attention to the manner in which it has been taught, and 
the different methods of teaching it. 

Grammar Poorly Taught. — Grammar has been more 
poorly taught than any other branch in the public schools. 
It has been made too abstract and theoretical. It has been 
taught as a matter of memory, and not of judgment and 
understanding. It has been a committing and repeating of 
definitions, and not a study of the relation of words in sen- 
tences. It has been a study of text-books on grammar instead 
of a study of the subject of grammar. It has been a memor- 
izing of abstract definitions and rules, instead of a practical 
application of them to the improvement of a pupil's language. 
It has been a worry and a waste of time and patience ; and a 
labor barren of adequate results. We believe we are correct 
in saying that more than three-fourths of the time spent in the 
study of grammar in the public schools, has been worse than 
wasted. 

The result of such teaching is that the pupils of our com- 
mon schools go out with a mucli better Icnowledge of arithme- 
tic, geography, etc., than of grammar. Besides this, the 
methods of teaching have given pupils wrong ideas of the sub- 
ject and incorrect methods of studying it. Taught by requir- 



234 METHODS OF TEACHING, 

ing pupils to commit and recite definitions, they have come 
to look at the gi*ammar of language through the definitions 
rather than at the definitions through language. Pupils thus 
taught not only obtain confused notions of grammar, but 
often acquire a dislike and even a disgust for the subject. 

These errors in teaching grammar arise from two sources ; 
the defects of our text-books and the incompetency of 
teachers. The books have been defective on account of 
their beginning with definitions instead of exercises to lead 
to definitions. They have presented the matter too ab- 
stractly. They have not aimed to lead the pupil to applj^ 
his knowledge of the subject. They hav-e not been pro- 
perly graded ; and have introduced dififlculties before the 
pupil was prepared for them. They have been constructed on 
the deductive method of teaching, instead of the inductive 
method, as all primarj' grammars should be. A change, 
however, is taking place in this respect; some of the more 
recent text-books on primary grammar being a great improve- 
ment on the old ones. 

The incompetenc}' of teachers, stated as the second cause 
of this poor teaching, has been not so much in their defective 
knowledge of grammar as in their defective methods of teach- 
ing it. Teachers of the public schools usually know enough 
grammar for their work, but they do not know how to teach 
it. Having been incorrectly instructed themselves, and hav- 
ing received no instruction in the true method of teaching it, 
they reproduce the same faulty methods in their own work, 
and thus the evil is perpetuated. 

The difficulty which pupils experience in learning grammar 
is entirely unnecessary. When properly taught, grammar is 
one of the easier studies of the common school course. In- 
trinsically, the elements of grammar arc less difficult than the 
elements of arithmetic: a knowledge of grammar, such as is 
contained in an ordinary common school text-book, is much 
more readily acquired than the same amount of arithmetic. 



TEACHING ENGLISH GRAMMAR. 235 

Grammar can also be made one of the most interesting studies 
of the piil)lic scliool, by teaching it according to a proper 
method. I have never seen children more interested in any 
classes than in the primary grammar class when correctly 
taught. 

Methods of Teaclmig. — There are two distinct methods of 
teaclung grammar ; the Synthetic or Etymological Method, 
and the Analytic or Logical Method. The Synthetic or Ety- 
mological method begins with the words, regarded as units of 
lanyaage, and proceeds to sentences. It regards the words as 
paints of speec/i, denoting names, actions, qualities, etc., and 
not as logical elements of thought. It is called Synthetic be- 
cause it proceeds from words to their combination in sen- 
tences. It is Ctilled Etymological because it deals with the 
parts of speech as words. 

The Analytical or Logical method of teaching grammar 
begins with the sentence as the unit of language, ixnd analyzes 
it into its thought elements. It considers the sentence as con- 
sisting of two principal elements, the subject and predicate, 
passes from these to subordinate and connective elements, and 
at last reaches the words as parts of speech. It first regards 
words not as parts of speech, but as expressing the logical ele- 
ments of which a sentence is composed. It is called Analyt- 
ical, because it passes from the sentence as a whole to the parts 
composing it. It is called Logical, because it deals with the 
h)gical elements out of which sentences are composed. 

The difference between these two methods is radical and 
important. Thus, by the former method, a noun is taught as 
a name; by the latter method it is regarded as expressing 
that of which something is said. By the former method a 
verb is an action-word ; by the latter method, it expresses 
ivhat is affirmed or asserted of the subject. An adjective, by 
tlie former method, is the name of a qualiti/ of an object ; by 
tlie latter method it is regarded as a word which limits the 
extent of a general conception or the application of a general 



236 METHODS OF TEACHING. 

term. Thus, by the logical method, good, in the expression^ 
good boys, is not regarded as expressing the qualily or kind 
of boys, but as limiting the concept boys to a portion of its 
extent, or the term boys to i^art of the class. So the aduerb 
limits the general action to some particular action : thus, in the 
sentence. The bird flies swiftly, the flying, which, without the 
adverb swiftly, would include all kinds of flying, is here limited 
to a particular kind of flying ; namely, swift flying. By the 
Etymological method, the preposition is taught as expressing 
the relation of objects ; by the Logical method it is taught as 
the connecting imrt of an adjunct or subordinate element. 

It should be observed that the two methods are not dis- 
tinguished merely by one beginning and the other not begin- 
ning with a sentence. We may begin with a sentence and 
teach by the etymological method, by regarding the Avords of 
the sentence as parts of speech. In teaching by the synthetic 
method we should use the sentence as well as by the analytic 
method. The essential ditlerence is not in the use or non-use 
of the sentence, but in the manner of using it. In one case we 
begin with the words as parts of speech ; in the other case Ave 
begin with the logical elements of a sentence, and come down 
to the Avords as parts of speech through these logical elements. 

The Synthetic method is to be preferred in teaching begin- 
ners. It is simpler and much more readily understood by 
yoimg pupils. It coincides also with the natural method by 
which they learn language ; first words, then sentences. A 
little child in beginning language, begins with words as the 
names of objects, rather than with sentences or propositions. 
Its adjectives are at first the names of qualities rather than 
limiting elements of general conceptions. 

This method is preferred also because it follows the law, 
from the particular to the general. "Grammatical Anal^'sis" 
is, to a large extent, a generalization of the principles of ety- 
mological grammar. Thus", at first, Ave see that a single word 
is a part of speech, as an adjective; and later Ave learn that a 



TEACHING ENGLISH GRAMMAR, 237 

phrase or a clause may be used as an adjective, and is thus an 
adjective element. The same is true for the noun, the adverb, 
etc. ; in each case there is a generalization from the use of 
tvords, to the similar use of phrases and clauses. 

In actual practice, we should begin with the synthetic 
method, and after la3'ing a fair foundation in the elementary 
ideas, we should introduce the analj'tical method gradually, as 
we find that the pupils are prepared to understand it. This 
will correspond with the historical development of the sub- 
ject, for ''Analysis" iu grammar is of recent origin; and was 
developed by an extension and generalization of the use of 
the parts of speech. 

Pi'iiictples of Teaching Grammar. — In teaching gram- 
mar by either of th'ese two methods, the teacher should be 
guided in his work by the following principles of instruction: 

1. Teach first by means of oral exercises.' Do not begin b^'" 
having pupils stud}' definitions from a text-book. No gram- 
mar-book is needed for several months, with a class beginning 
grammar. In an ordinary- common school, I should use no 
text-book on the subject for at least six months or a year. A 
school reader may be used for examples of parts of speech, 
for parsing, etc. A text-book in grammar is a positive dis- 
advantage to a beginner. It seems to stand as a partition 
wall between the pupil's mind and the subject. It causes hi_m 
to " see through a glass" very darklj- that which is simple and 
clear without the book. 

2. Teach grammar from language and not from definitions. 
The old way was to begin with definitions ; the correct method 
is to begin with language. In this way the pupil will see and 
understand the grammatical use of words, while by the old 
method he recited their use without understanding it. By 
'the former method, he depends on what the book says ; by the 
latter method, he learns to depend on his own judgment in 
determining the nature and relation of words. In one case, 
he looks at grammar through the definitions; in the other case 



238 METHODS OF TEACHING/ 

he looks at grammar through the nature of the subject itself 
In the former case, grammar is too much a matter of memory; 
in the latter case, it is a matter of the judgment and the un- 
derstanding. Let grammar, therefore, be taught from lan- 
guage, as it was originally developed by those who first inves- 
tigated it. 

An additional reason for teaching primary grammar from 
language without a text-book, is that the proper study of the 
subject is especiall}' an act of the judgment. There are very 
few things to commit to memory in elementary grammar. 
There are a few technical terms which are readil^' remembered 
when the pupil has the ideas which they express. What we 
especially need is to examine language and notice the rela- 
tions of words ; and not to commit and recite definitions. 
There is no other study in the public school that so little needs 
a text-book as the first lessons in grammar ; and assuredly 
there is no study in which the text-book is so much of a hind- 
rance to the beginner as this. Some of the most successful 
teachers of advanced classes in grammar use an edition of 
some of the favorite poems of our eminent authors as the text- 
book for the lesson, while the real text-book is used onlj^ as a 
work of reference. 

3. Make the sentence the basis of grammatical instruction. 
Though we begin with words, we should pass as soon as pos- 
sible to sentences, and study the words with respect to their 
relations in sentences. Grammar treats of the sentential use 
of words, and it is only by viewing their relations in sentences 
that we can understand their grammatical meaning and use. 
In teaching grammar, therefore, the sentence is to be regarded 
as the unit of reference. But though we make use of the sen- 
tence in instruction, we are to consider, first, not the logical 
use of the Avords in it, but their etymological use. The words* 
in the sentence are to be regarded as etj'mological elements 
expressing names, actions, etc., and not the logical elements 
of which sentences are composed. 



TEACHING ENGLISH GRAM MA K. 239 

4. Make the subject practical. We should require the 
pupils to use good grammar ; to apply what they learn in 
moulding and correcting their own speech. We should 
excite an interest among pupils in the use of correct lan- 
guage, and in correcting their mistakes. Have them bring- 
in false syntax heard in the school-room and on the play- 
ground. Let the teacher be careful to use correct language 
himself, as an example to his pupils. 

5. The course in grammar should be jireceded by a course 
of instruction in Language Lessons. The basis of instruction 
in grammar is language, and a pupil should have some lessons 
in language before he begins the subject of technical grammar. 
Such a course of lessons is indicated under the methods of 
teaching Composition. 

Time to Bet/in — The time to begin grammar depends 
upon the manner in which it is taught. If presented induc- 
tively, with oral* exercises, the pupil ma}^ begin the study at 
nine or ten years of age. The average age for the pupils of 
our common schools is probably about ten or twelve. If, 
however, grammar is taught by the old method from the text- 
book, it should not be commenced before the age of fifteen or 
sixteen. 

Division of Subject. — For the purpose of instruction, 
grammar may be divided into Primary Grammar and Ad- 
vanced Grammar. For Primary Grammar, the S3aitlietic or 
etymological method of teaching is employed as the basis of 
instruction ; in Advanced Grammar the analytic or logical 
method should be made more prominent. We shall indicate 
a course of instruction in both. 

II. Method of Teaching Primary Grammar. 
By Primary Grammar is meant such a course of instruction 
in grammar as shall present the fundamental facts and princi- 
ples of the science. It is designed to lay the foundation of 
grammatical knowledge, but docs not extend to the higher 



240 METHODS OF TEACHING. 

philosophical principles of the science, nor discuss the anoma- 
lies of construction, etc. 

Principles of Instruction. — There are several principles 
of instruction that should be made especially prominent in a 
l)rimary course in grammar. They are principles that have 
been previously announced ; but so important are the^^, and 
so often are they violated in grammatical instruction, that we 
repeat them here. 

1. Teach first the idea and then the expression of it. This 
principle is of especial importance in teaching grammar. The 
old way was to teach the expression first, and often the pupil 
did not get the idea at all. Both teachers and pupils have 
used the expressions, "govern," ''relates to," "qualifies," 
"modifies," etc., for years, without ever thinking what they 
meant. The majority of teachers of whom we have inquired, 
What do you mean by " prepositions govern the objective 
case ? " could give no intelligent explanation of its meaning. 
Do not, therefore, begin with the definition as the statement 
of the idea, but present the idea first, and then lead the 
pupils to the expression of it. 

2. Teach pupils to discover the idea you wish to exjjress. 
The old way was to tell the pupil everything ; the better way 
is to allow him to discover all he can for himself. This is the 
inductive method of instruction, and grammar is one of the 
ver^' best studies in which to apply the inductive method. It 
will make the pupil a thinker in grammar, independent of the 
teacher or text-book. 

3. Let the pjrimary aim he grammatical ideas rather than 
gramviatical expressions. Care not so much for the defini- 
tions as for the idea to be defined. Do not require definitions 
until the idea is clearly developed in the mind of the learner, 
and let the definition flow from the natural expression of the 
idea. 

4. Do not burden the memory icith g ram matical forms. A 
general fault in teaching grammar is that the subject is made 



TEACIIIXG ENGLISH GRAMMAR. 24:1 

too formal. Too much attention is paid to the manner of 
expressing grammatical ideas. In Primary Grammar, the 
forms of parsing and analysis should be very simple. We 
should depend more upon asking pupils questions in language , 
than upon their giving any set forms of expression. 

The Order of Instruction in this subject, in accordance with 
these principles, is as follows : 1. The Idea ; 2. The Name ; 
3. The Definition ; 4. Exercises. 

The Course of Instruction. — The Course of Instruction in 
Primary Grammar includes the following things : 1. The 
Parts of Speech; 2. The Properties and Inflections ; 3. The 
Classes of the Parts of Speech ; 4. The Rules of Construction ; 
5. The Elements of Parsing; 6. The Elements of Analysis ; 7. 
Correcting False Syntax, 

These are to be presented somewhat in the order named, 
but not entirely so. We should begin with the Parts of 
Speech, but the Classes and the Inflections may be taught 
somewhat together ; and the Elements of Parsing, Analj'sis, 
and the Correcting of False S3nitax, should be introduced 
gradually as the pupils are prepared for them. The above is 
a logical division, sliowing what is to be taught rather than 
the order in which the several things are to be presented. In 
presenting the subject, we shall first describe the method of 
teaching, and then follow the description with an inductive 
lesson, indicating how the pupil is led to the idea and its ex- 
pression, by appropriate questions. 

I. Parts of Speech. — We begin the instruction in grammar, 
by teaching the Parts of Speech. In order to prepare for 
this, we should give to the pupil a clear idea of an object 
and a word. This can be done by showing them an object, 
asking its name, and calling attention to that wdiich we hear 
spoken, or see written. The lesson suggested is as follows: 

Model Lesson.— Teacher, holding up a book, a, knife, etc., saj'-s, What 
"is this? Pupil. A book. T. This '? P. A knife. T. What do we call all 
these things we can see, touch, etc.? P. Objects. T. What do we call 
11 



242 METHODS OF TKACllING. 

those things we hear when we speak? P. 'Words. T. Are there any 
words besides those we hear ? P. Yes, words we can see. P. What 
shall we call the words we can see ? P. Seen words. T. Since we write 
those words, what may we call them ? P. Written words. T. What may 
we call the words we hear? P. Heard words. T. Since we speak them, 
what "kind of words may we call them? P. Spoken words. T. How 
many kinds of words then have we? P. Two kinds; spoken words and 
written words. 

The Noun. — To teach a Noun, present several objects to the 
pupil, have him name them, write these names on the board, 
and lead him to call them object-words; then to define an 
object-word, and then give him the term noiui as meaning the 
same as object-word, and have him define a noun. Then give 
exercises, requiring him to select nouns from a book, and to 
give examples of nouns. Then teach that the names of per- 
sons, places, etc., begin with a capital letter. 

Model Lesson. — Teacher. What is this I hold in my book. 

hand? Papil. A book. T. What is this? P. A knife. ^^/«; 

r. This? P. A pencil. 2'. I will write these names on S2mo 

the bo.ird; what are these in my hands? P. Objects. 
T. What are these on the board ? P. Words. 2\ What are these 
words the names of? P. The names of objects. T. Since they are the 
names of objects, what kind of words may we call them? P. Object- 
words. T. What then is an object- word? P. An object-word is the name 
of an object. 

They have thus been led to the idea of an object-word, to 
name it themselves, and to make their ow^n definition of it. 
The next step is to require them to name and write object- 
words, and to have them point out object-words in the reader. 
After they are fiimiliar with object-words, then introduce the 
name noun. The exercise is as follows : 

Model Lesson. — Teacher. What do we call the names of objects? Pupil. 
Object-words. T. I will give you a shorter word that means the same as 
object-word; it is noun; what is it ? P. Noun. T. What then is a noun ? 
P. A noun is an object-word. T. And what is an object-word? P. An 
object- word is the name of an object. 7'. Wliat then is a n()u«.? P. A 
noun is the name of an object. 

The Verb. — To teach the Verb, we call the pupil's attention 



runs, 
plays. 

SilKJS. 

eats. 

drinks. 

sleeps. 



TKACIIIXG ENGLISH GRAMMAR. . 21-3 

to the actionn of some object, write a list of words expressing 
action upon the board, lead the pupils to call them action- 
words, and define an action-word, and then, after they are 
familiar with the idea and name, introduce the term verb as 
meaning the same as action-ioord, and lead them to define it, 
and give them a drill on the verb and the noun. 

Model Lesson. — Teacher. Name some of the actions of a child. Pupil. 
A child runs, plays, sings, eats, drinks, sleeps, etc. 
7'. Very well, I will write these on the board in 
a column ; what are these words the names of? P. 
The names of acft'o/is. 7'. If they were the names Child 

oi objects, what should we call them ? P. Object- 
words. T. Since they are the names of actions, 
Avhat may we call them? P. Action-icords. T. 

What then is an action-word? P. \n action- word is the name of an 
action. T. Very well ; there is a little word that means the same as 
action-word ; it is verb ; what is it? P. Verb. T. What then is a verb? 
P. A verb is an action-tcord. T. And what is an action-word? P. The 
name of an action. 7'. How then may we define a verb ? P. A verb is 
the name of an action ; or, A verb is a ioord that expiresses action. 

Exercises. —1. Name actions of different oTijects. 2. Name objects that 
can do different actions. 3. Select nouns and verbs in tlje reader. 

The verb may also be taught as a doiag-xoord instead of an 
action-word, by asking what a child can do. After the pupils 
are familiar with the use of the verb as the name of an action, 
thev may be led to see that it is used in a^.^erting something, 
and may thus be called an asser ting-word, or a word used in 
making an assertion. 

lite Sentence. — We should next unite the noun and vei-l) 
into sentences, and give the pupil an idea of the sentence. 
We then teach the three kinds. of sentences, — the telling or 
declarative sentence, the asking or interrogative sentence, and 
the commanding or imperative sentence. We then, teach 
them to write sentences, observing these three rules: 1. A 
sentence begins with a capital letter ; 2. A declarative or .in 
imperative sentence ends with a period ; 3. An interrogiitive 
sentence ends with an interrogation point. 



214 iMETHODS OF TEACHING. 

Model Lesson. — Teacher, writing the word John on the board, asks what 
he has written on the board. Pupil. The word John. T. Tell me some- 
thing John does. P. John icalks, John talks, John sings, etc. 7\, writ- 
ing them on the board, saj'S, Such expressions as these, containing a 
noun and a verb, in which the verb tells something of the noun, are 
called sentences. Make some sentences about Mary, a bird, a horse, etc. 
T. What might a sentence which tells something, be called ? P. A tell- 
ing sentence. T., writing, Can John loalk? says, Does this tell anything 
about John ? P. No, sir, it asks a question. T. Very well, such a com- 
bination of a noun and a verb is also called a sentence. Since it asks a 
question, what kind of a sentence may we call it? P. An asking sen- 
tence. T., writing, John, \oalk fast, may by similar questions, lead 
the pupils to call it a commanding sentenced 

The Adjective. — In teaching the Adjective, we first lead 
to the idea of quality. We do this b}^ comparing objects, and 
having pupils name the ditferences, and telling them these are 
called the qualitiea of the objects. We tlien get a list of the 
qualities of an object, and then lead the pupils to call the 
words quality-words, or qaality-object-words, and define the 
same ; we then introduce the term adjective, and have tliem 
define it. Before giving the word adjective it may be well to 
lead pupils to call them adnouns, since they are added to 
nouns. 

Model Lesson. — Teacher, holding up two objects, as a pencil and card, 
"What have I in my hands ? Pupils. Pencil and card. T. Do they look 
alike? P. No, sir. T. How do they differ? P. One is round, the other 
is flat ; one is black, the other is lohitc; etc. T. Very well; these things 
in which objects differ are called qualities of objects; what are they 
called? P. Qualities of objects. T'. Name some qualities of an apple.- 
P. Sweet, sour, red, yelloic, mellow, ripe, etc. T. We will 
write these in a column on the board ; now what are these sweet. 
words the names of? P. Qualities of objects. T. If they l'.'J^'' 
were the names of objects, what kind of words should we yelloio. 
call them ? P Object-words. T. Since they are the mellow. 
names of qualities, what shall we call them? P. Quality- 
words. T. Since they belong to objects, what kind of quality words may 
we call them ? P. Quality-object-icords. T. What then is a quality-oh- 
ject-word? P. A quality-object- word is the name of a quality of an ob- 
ject. T. There is another word which means the same as quality -object 



TEACniXG ENGLISH GRAMMAR. 245 

word; it is adjective; what is it? P. Adjective. T. What, then, is an 
adjective ? P. An adjective is a qiiality-object-word. T. And wliut -is a 
quality-ohject-iDord f P. The name of a quality of an object. T. Wliat 
then is an adjective f P. An adjective is the name of a quality of an object. 
Sliow also how to lead the pupil to call them adnouns. 

Exercises. — 1. Name the qualities of objects; 2. Name objects having 
certain qualities; 3. Write sentences containing given nouns, verbs, and 
adjectives; 4. Point out nouns, verbs, and adjectives in the reading book. 

Tlie Adverb. — We taught the Adjective by comparing ob- 
jects ; we should teach the Adverb by comiMring actions., 
since the adve?-b bears the same relation to actions that the 
adjective does to objects. We begin by comparing actions, 
obtain a number of words which distinguish them, write these 
words upon the board, and lead the pupil to call them qual- 
ity-actio7i-ivords, and define the same; and then introduce the 
tevm adverb by showing that the qualit3'-action-word is added 
to a verb, and lead them to define it. 

3Iodcl Lesson. — TcacJier, moving his hand, inquires. What am I doing? 
Pupil. Moving your hand. T. Look and see if these motions are alike: 
how does it move now ? P. Sloicly. T. How does it 
move now ? P. Fast, or quickly. T. How does it move sloirly. 
now ? P. Upward. T. How does it move now 1 P. Vlyward 
Dowmcard. T. Are these motions alike ? P. No, sir. downward. 
T. What words distinguish these actions? P. Sloicly, 
quickly, xqncard, downward. T. What did we call those things in which 
objects differed? P. Qualities of objects. T. What shall we call those 
things in which actions differ ? P. Qualities of actions. T. What shall 
we call those words t'lat name the qualities of actions ? P. Qucdity- 
action-iDords. T. What then is a, qunlity-action-word? etc., etc. To lead 
to the term adverb write " hand moves slowly" on the board. T. What 
is slowly? T. To what word is ^AovrXj added, hand ov moves? What 
part of speech is moves? To what part of speech then is slowly added? 
If it is added to a verb, what may we call it? P. Added to a verb? T. 
Yes, or adverb; what then is an adverb ? etc. 

In this wa}^ the adverb is first taught as a word which dis- 
tinguishes actions. After the pupil is entirely familiar with 
this idea, the use of the adverb as distinguishing the qualities 
of objects should be presented. This may be done by com- 



246 



METHODS OF TEACHING. 



paring hvo qualities, as we did actions, and thus obtaining a 
list of words wliicli distinguish qualities. The pupil is then 
to be told that these words are also called adverbs. Let the 
P<-udent-teacher give an exercise from the description. 

After this idea is clearly in the mind, the office of the ad- 
verb as distinguishing between the qualities of actions, or as 
limiting an adverb, should be taught. This is done by com- 
paring the qualities of actions, thus the qualitj^ slowly may be 
compared, giving us very slowly, rather slowly, more slowly, 
etc., and getting a list of words which distinguish qualities of 
actions, and telling the pupil that these are also called ad- 
verbs. The manner of forming adverbs from adjectives by 
adding like or its contraction ^//,thus, sweet-like, siveetly, etc., 
may also be shown. Let the student-teacher give the lesson. 

In this way the adverb, in its three-fold use, may be under- 
standingly taught. With the more adA^anced pupils, the 
question may be raised, why the same part of speech, the ad- 
verb, should have been used to perform these three offices, 
namely, to distinguish actions, qualities of objects, and quali- 
ties of actions ; and why we should not have another part of 
speech to distinguish qualities of objects and actions. 

Another way of teaching the adverb recommended by some 
teachers, is to show that it expresses how, when, and where, 
and introduce it as a hoiv, when, or tvhei-e word; but the 
method already explained is preferred, because it shows the 
real nature and office of the word, which the other does not. 

The Pronoun. — We teach the Pronoun by showing the 
pupil that words are used for nouns. We get a list of such 
words on the board, drawn from actual use in language, and 
lead the pupils to call them /or'-noims, and define a for-noun, 
as a word used for a noun. Then tell them that there is a 
word, pro, derived from an old language, which means the 
same as /or, and lead them to substitute it for the word for, 
getting tlie word pronoun; and then lead them to define a pro- 
noun; and continue the exercises on the parts of speech. 



TEACHING ENGLISH GRAMMAR. 247 

Model Lesson.— Teacher, writing on the board the sentence, "Give 
John John's book, " says. How else may this be expressed? Pupil. 
Give John /«■« book. T. How may "Give Mary Mary's boolc," be 
otherwise expressed '? P. Give Mary her book. T. For what word do 
Ave use his? P. For John. T. What part of speech is John? P. A 
noun. T. For wliat then do we use /ws .? P. For a noun. T. What may 
we call words wliicb we use for nouns? P. For-nouns. T. What then 
is afor-noun? P. Kfor-noun is a word used for a noun. T. If we use 
the word j^ro, which means /o?', in place of for, what -wiW for-noun be- 
come? P. Pronoun. T. What then is apro;io;m .? P. A pronoun is a 
word used for a noun, etc. Keep up the review in exercises as before. 

The Conjunction. — The Conjunction raixy be taught \)y 
leading pupils to see its use in joining words, and then 
leading them to its name as a conjoining-word ., from which 
they can be led to the term conjunction. Then lead to the 
definition and give an exercise on all the parts of speech, as 
previously indicated. For these exercises, let it be remem- 
bered, we should use language spoken by the teacher, or 
written upon the board, or found in theprimar}" reader. 

Model Lesson. — Teacher, writing on the board, "John can read; John 
can write" — ^.asks, How else can this be expressed ? Pupil. John can read 
and write. T. What word is used to join read and write ? P. The word 
and. T. What kind of a word may it be called ? P. A joining-word. 
T. Yes, or a conjoining -word. T. What then is & conjoining -loord? P. A 
conjoining-word is a word that joins or unites other words. T. If the 
word conjunction is used for conjoining-toord, what is a conjunction? etc. 
In a similar manner we may show that the conjunction also unites 
sentences. 

The Preposition. — To teach the Preposition., we show the 
pupil that some words express the relation of objects, and that 
such words may be called relation-ivords ; then lead to a defi- 
nition of relation-words ; then introduce the term preposition 
in place of relaiion-word., and lead to a definition of 2)reposi- 
tion, and continue the exercises as before. In this exercise, 
the term relation, which is new to the pupil, is best explained 
by using it in the lesson. 

Model Lesson. — Teacher. Standing by a table and having a book in his 
hand. What object is this? Pupil. A table. T. What object is this? P. 



248 



METHODS OF TEACHING. 



on. 

under. 

over. 

above. 

beside. 



A book. T., placing the book on the table, Where is the book now ? P. 

On the table. T. Where is the book now ? P. Under the 

table. T. Where is the book now ? P. Oyer the table, etc. 

T. Placing the l)ook on the table again. What little word 

shows the relation of the book to the table now? P. On. 

T. What little word shows the relation of the book to the 

table now ? P. Under ; etc. T. Here we have a list of 

words which do what ? P. Show the relation of objects. T. What shall 

we call these words that show the relation of objects? P. Belation-words. 

T. What then is a relation-icord? etc. T. The word preposition is used 

for relation-word ; what then is a preposition ? etc. 

Tlie Interjection — The Interjection should be taught as a 
feeling- or emotion-word. Ask what words we sometimes use 
when we feel very sad, or very glad, or when feeling surprised, 
etc., and get a list of words like oh., ah., alas, hurrah, pshaiv, 
etc. Then, since these express feelings or emotions, they may 
be called feeling- or emotion-words. Then lead to the defini- 
tion, etc. At last lead to the idea that they are interjected, 
or thrown in between other words, and may be called interjec- 
tions, and lead to the definition ; and then drill them on exer- 
cises on all the parts of speech, similar to the manner pre- 
viously suggested. 

II. Properties of Parts of Speech. — By the Properties of 
the parts of speech are meant those things which belong to or 
are peculiar to the different parts of speech. They include 
the Number, Person, Gender, and Case of nouns and pro- 
nouns; the Number, Person, Mood, Tense and Voice of verbs; 
and the Comparison of adjectives and adverbs. These proper- 
ties are also called Inflections, because there is a bending or 
change of the word from its original form or meaning. 

Idea of Property — The first thing to teach under Propei'- 
ties, is to lead a pu])il to a clear idea of what is meant hy a 
property of a part of speech. Nine-tenths of the pupils in 
grammar who use the term property, never stop to think wdiat 
it means. To present the idea of property, take two objects, 
as a pencil and card, call attention to their qualities, lead to 



TEACHING ENGLISH GRAMMAR. 249 

the idea that these qualities belong to the objects, lead them to 
tell you that that which belongs to any person is his property, 
and hence those things which belong to words and distinguish 
thein are called properties of those words. 

Model Lesson. — Teacher. What are these olyects? Pupil. K pencil and 
card. T. Name some of their qualities. T. To which object does the 
quality w/aY^ belong; to which object does the quality black belong? 
T. The things which bslong to your father — his farm, horse, etc.— are 
called liis what? P. His property. T. What then may we call ti;Ose 
things that belong to objects? P. The 2>roperties of objects. T. What 
may we call the things which belong to words? P. The properties of 
words. T. What then is a property of a part of speech? etc. 

We can teach the meaning of an inflection by taking a word like ahhot, 
which expresses a man, and show that it changes to abbess to express a 
woman ; that Sec changes to boxes to express the plural ; etc. Then lead 
them to see that such changes or bendings of words to express a change 
of thought, are called bendings or inflections. Let the student-teacher 
show the method by a lesson. 

Properties of Nouns and Pronouns. — We shall first con- 
sider the properties of Nouns and Pronouns, including Num- 
ber, Person, Gender, and Case. 

Ninnber, — To teach Number, we lead the pupil to see that 
words have one form for one thing and another form for more 
than one thing ; and then since one, two, three, etc., are num- 
bers, this property of nouns may appropriately be called the 
Number of nouns ; and the pupils may be led to define it. "We 
then lead them to see that there are only two numbers, since 
there are onW two forms, one form for one thing and another 
form for more than one thing. We ma^^ then lead them to 
call one single number and the other many number, from which 
we pass to singular and plural. 

We may then lead to the Rule for number, by leading them 
to see that we sometimes add an s to the singular and some- 
times es, and sometimes change the form of the word, in form- 
ing the plural. 

Model Lesson. — Teacher. What have I in my hand? Pupil. K hook, 
T. How many books ? P. One book. T. How many have I now ? P, 
11* 



250 



METHODS OF TEACHING. 



Two books. T. How many now ? P. Three books. The teacher will 
then write on the board, " I have one book, " " I have two boolis, " "I 
have three books," etc. T. Which is the noun in these sentences? T. 
How many forms lias it 1 P. Two forms, hook and books. T. What is 
its form for one thing ? T. What is its form for more than one thing ? 
T. We have then discovered this property of a noun, — that it has one 
form for one thing and another form for more than one thing — let us see 
now what we shall call this property. T. What are one, two, three, etc., 
in arithmetic. P. Numbers. T. What might we call this property of a 
noun by which it has one form for one thing and another form for more 
than one thing ? P. The number of a noun. T. What then is the number 
of a noun ? P. Number is that property of a noun by which it has one 
form for one thing and another form for more than one thing, T. Let 
us now see how many numbers nouns have. T. How many forms has 
the noun book ? P. Two forms. T. How many numbers then are there ? 
P. Two numbers. T. If there were three forms, one form for one thing, 
another form for two things, and another form for more than two 
things, how many numbers would there be ? P. Three numbers. 

T. Let us see now what we shall call these two numbers. T. When a 
horse is hitched up alone, what kind of a harness do you use ? P. A 
single harness. T. When there is one thing alone, then what may you 
call it? P. A single thing. T. What may we then call this number of 
a word which represents a single thing ? P. Single number. T. Very 
well ; that is right ; now let us see what we shall call the other number. 
T. When a boy has a "whole lot" of marbles, he would say he had a 

great what marbles ? P. A great many marbles. T. IMore than one 

thing then may be called what ? P. Many things. T. This number, 
then, that means more than one, may be called what number? P. 
Many number. T. What are the two numbers then ? P. Single number 
and many number. The pupils may then be led to define each, and sub- 
sequently the words singular and plural may be introduced. 

They ma3^ then be led to see that iu words like hook we add 
s to form the plural, and state it as a rnle. They may then he 
led to see that in other words, as in box., we add es to form 
the plural, and state it as a rule. They raaj^ then be led to 
see that we sometimes change the form of the word to form 
the plural, as ??if/», ?nfin, 0J7, oxen., etc. The pupils should then 
be drilled on forming plurals; and also make a list of the per- 
Honal pronouns classed with respect to number, as these will 
be needed in some of the exercises which follow. 



TEACHING ENGLISH GRAMMAR. 251 

Taught in this way, the pupils will see that though there are 
many uumbers in arithmetic, there are only two numbers in 
grammar, since there ai'e only two forms of woi'ds to distin- 
guish the number of objects. They can be told that in some 
languages, as the Greek, there is one form for a single thing, 
another form for two things, and another form for more than 
two things, giving three numbers in grammar — the singular, 
the dual., and the jjlural. 

Person. — To teach Person, we first lead the pupils to see 
that a noun may represent three distinct persons — the person 
speaking, the person spoken to, and the person spoken of. We 
then lead them to call this property of wovwis person; then lead 
them to a definition of the person as that property of a noun 
b}^ which it represents the person speaking, the person spoken 
to, and the person spoken of. We then lead them to see that 
there are three grammatical persons, and that the}- are appro- 
priately- distinguished as first person, second person, and 
third person. To do- this', "we lead them to see that the first 
thing necessary for something to be said is Si person speaking, 
the second condition is some one to speak to, and the third con- 
dition is some one or something to speak of; hence the name 
of the speaker may be called ih.e first person, the name of the 
person spoken to, the second jjerson, and the name of the pei'- 
son or thing spoken of, the third person. 

The pupils should then be required to point out the person 
of nouns and pronouns, use nolms and pronouns of a given 
person in constructing sentences, and be drilled on exercises 
similar to those already suggested. They should also be re- 
quired to make a list of pronouns arranged according to 
person. 

Let the student of this book be required to translate the 
above description into an inductive lesson, such as is given 
under the previous subjects. The following three sentences 
may be used in giving the lesson: "I, John, am here;" 
" John, come here ; " " John is here." 



252 METHODS OF TEACHING. 

Case. — The subject of Case is regarded as very difFicult for 
young pupils; but, if properly presented, it is quite readily 
understood. We should first teach the nominative and object- 
ive cases together, then the possessive case, and then the 
objective case after the preposition. We shall describe the 
lesson briefly. 

The teacher will write on the board, John strikes William, 
call attention to the action, ask who does the action, who 
receives the action, then ask if they both bear the same i'ela- 
^io^ to the action ; what relation John bears to the action, 
having them say he is the doer of it ; what relation William 
sustains to the action, leading them to say the object of tlie 
action; then tell them that this property of words sustaining 
different relations to an action is called Case, and lead them 
to define case ; then lead them to call John the doer case and 
William the object case, and define each ; after which he can 
introduce the terms nominative and objective. 

The possessive case can be easily taught by the relation of 
ownership or possession. The next step is to lead to the dif- 
ferent case forms of the personal pronouns. A list of these 
should be made, classed according to case ; and the pupil be 
drilled on them until he knows them hy sight, independently 
of their relation in .the sentence. 

The next step is to teach the objective case after the prepo- 
sition. This needs especial notice, as it is not at all apparent 
to the learner that in the sentence, " He gave it to John," 
John is in the objective case. Indeed, if the teacher should 
take the two sentences, " John has the book," and " I gave 
the book to John," and ask what case is John in the first sen- 
tence, and then what case is John in the second sentence, the 
pupils would say nominative in both. This shows that it is 
not evident to a beginner that prepositions require the object- 
ive case. AVe should, therefore, teach the objective case after a 
preposition hy the use of the pronoun. Let the pupil see that 
in the sentence, " I gave the book to John," we cannot say 



TEACHING ENGLISH GRAMMAR. 253 

"to /;.e," nor "to /u.s," but ai'e required to say, "to him,^^ 
which is the objective form ; lience Jolin, which is represented 
by him, must be in tlae objective case. Let the pupil then be 
drilled on case by pointing out the ease of words in sentences, 
constructing sentences with given cases, etc., as before sug- 
gested. The student-teacher should be required to present 
this description in an inductive lesson, like those previously 
given. 

Gender. — Gender is easily taught. We first call attention 
to the ditference of sex in animals, and the absence of sex in 
other objects. We then show that some words change their 
form to express males and females, which property is called the 
gender of nouns and px-onouns. Then lead them to define gen- 
der, to see that there are two genders, since there are two sexes, 
and lead them to name and define each. Then lead them to 
see that the words which apply to objects without sex have 
no gender, or are in neither gender, or neuter gender ; and 
also that those words which are common to both males and 
females may be said to be in common gender. The main point 
of difficulty is to distinguish sex, which is the attribute of 
objects, from gender, which is a property of words. Give 
abundant exercises as before suggested. The student-teacher 
will give the lesson like the models presented. 

Properties of the Yerb. — We shall now show how to 
teach the properties of the Verb to beginners in grammar. 
These properties are Number, Person, Mode, Tense, and 
Voice. The properties of Number and Person are derived 
properties, properties which the verb acquires from its sub- 
ject. The other properties are intrinsic, belonging to the 
verb per se. 

3Iode of Verbs. — To teach Mode, write on the board, 
" John studies his lesson," " John, study j'our lesson," and 
" John can study his lesson." Ask which sentence declares 
the action, which commands it, which expresses its possihiUty, 
then ask which part of speech expresses these three things. 



254 METHODS OF TEACHING 

Ask in what manner the verb expresses the act in the first 
sentence ; have them sa}-- it simply declares the act. Ask 
in what manner the verb expresses the act in the second sen- 
tence ; requiring them to say it commands the act ; etc. We 
thus discover the property that a verb may express an action 
in difFerent manners ; then inquire what we may call this 
property of the verb, and have them call it the manner of the 
verb. What then is the manner of a verb ? If we use the 
word Mode, which means the same as manner, what shall we 
call this property of the verb? Ans. The Mode of the verb. 
What then is the mode of a verb ? etc. 

The next point is to name the modes. In how man}' ways 
did we express the action? How many modes then are there? 
The first simi)ly declares or indicates the act, what mode then 
may we call it? Ans. The declaring or indicating m,ode. 
From this we lead to the declarative or indicative mode. 
The second commands the act ; lead pupils to call it the com- 
manding mode, and then give them the term imperative. The 
third expresses the possibility of the act ; lead them to call it 
the jyossible mode, and then give them the term potential, as 
meaning the same thing. 

The subjunctive mode is so nearly obsolete that it need not 
be taught; and the infinitive may be taught by its form; or, 
what is better, be called an infinitive, and not regarded as a 
mode of the verb. The participle may be taught in the same 
manner. The student-teacher should be required to present 
the method of teaching mode in an inductive lesson. 

Tense of Verbs — To teach Tense we first call attention to 
the kinds of time — present, past, and future. We then write 
on the board — "John studies grammar," "John studied 
grammar," "John will study grammar;" and ask what time is 
expressed by each form of the verb, and thus discover that 
the verb can express the act as present, past, or future. ^ We 
then call attention to this property of a verb by which it ex- 
presses ditferent kinds of time, and lead the pupils to call it 



I 



TEACIIINGr ENGLISH GRAMMAR. 255 

the time of the verb. We then introduce the word tense, mean- 
ing the same as time ; lead them to call the property the tense 
of the verb, and then lead them to define tense. We then lead 
them to call the first, present tense, the second, past tense, and 
the t\nx(\, future tense, and require them to define each. 

The other tenses may also be easily taught. Show them 
that have studied, since it denotes the act as completed or 
perfected, may be called the completed or ■perfect tense; and 
since it expresses an action having a relation to the present 
time, it may be called the present perfect tense. Also that 
had studied, since it denotes an act completed at some past 
time, may be called the ^as^ |3er/ec^ tense. Also that shall or 
roill have studied, since it denotes an act completed at some 
future time, may be called the future perfect tense. The 
tenses of the potential mode may be tauglit arbitrarilj^ by 
their forms, since they do not express the distinctions of time 
as named. The student teacher will put the above in an in- 
ductive lesson. 

Number of the Verb. — The Number of verbs should be 
taught with reference to the number of their subjects, as the 
verb of itself has no numbei\ It is a property derived from 
its subject, and should so be presented to the learner. 

To teach the number of verbs, write a senteuce on the board, 
as " He reads the Bible," and under it " They read the Bible," 
and ask what change there is in the verb, and the reason for 
this change. Let the pupils see that the change in the num- 
ber of the subject causes a change in the form of the verb. 
They thus discover a property, that the verb changes its form 
when the subject changes its number ; and they may be led to 
call this property the number of the verb. Then lead them to 
define the number of a verb. 

Drill the class on the singular and plural forms; have them 
point out the forms in sentences, construct sentences with 
given numbers, correct mistakes heard in conversation with 
respect to the number of the verb, etc. Require them also to 



256 METHODS OF TEACHING. 

derive and state the rule of the agreement of the verb with 
its subject in number. 

Person of Verbs — The Person of the verb should be 
taught with reference to the person of its subject, as the verb 
in itself has no person, but derives it from its subject. 

To teach the person of verbs, write on the board, " He reads 
a book," and under it, " I read a book," and call attention to 
the change in the form of the verb. Then lead them to see 
that the subject has changed, not its number or gender., but 
its person ; and that we have thus discovered a property of a 
verb, that it changes Us form as its subject changes its person; 
and that this property maj' appropriately be called the person 
of the verb. Then lead them to define the person of a verb as 
that prop)erty by which it changes its form as its subject 
changes its person. Then drill the pupils on person, as pre- 
viously suggested. 

Voice of Verbs. — The Property of Voice, if it be taught at 
all, may be presented as follows : Write on the board, " John 
strikes William," and " William is struck by John." Lead 
the pupils to see that in the first sentence the verb expresses 
the subject as acting^ and in the second it represents the sub- 
ject as receiving the act. We thus discover a property of a 
verb, that it may represent its subject as acting or being acted 
upon. This property needs a name; what shall we call it? 
Call their attention to the fact that we. express things with 
the voice^ and that since the voice is a tcay of expressing 
things, this property of verbs by which they express the act 
in different ivays may be called voice. 

Then lead to the name of the two kinds of voice. Since the 
first expresses the subject as active, it may be called the 
active voice. Since the second expresses the subject as re- 
ceiving the action, it may be called the receiving voice ; or, 
since the woi*d passive means just the opposite of active, and 
the verb expresses its subject as not active, but passive, this 
second kind of voice may be called the passive voice. 



TEACHING ENGLISH GRAMMAR. 2o7 

Comparison. — The Comparison of adjectives and adverbs 
is ver}" easily taught, and we will not take space to present the 
subject here. Any teacher who has become thoroughly im- 
bued with the spirit of the concrete and inductive form of 
instruction used in the previous exercises, will have no 
trouble in presenting the subject, if he understands it himself. 

III. Classes of Parts of Speech. — The Classes of the 
Parts of Speech should next be presented. It might be 
thought that these should have preceded the Properties, but 
in several cases we need a knowledge of the properties in 
order to make the distinction of classes. In actual instruc- 
tion, they should be, to a certain extent, combined, which is 
left to the judgment of the teacher. It is more convenient to 
consider them separately in this work. Under each head we 
will describe the method of instruction, but the student- 
teacher should be required to present it in the form of an in- 
ductive lesson. The author of this work does not consider 
his pupils as prepared to teach any part of grammar until 
they can present an inductive lesson, showing just how the}' 
would proceed in their instruction. 

Classes of Konns. — The teacher, by appropriate examples 
and questions, will lead the pupil to see that some nouns 
apply to particular persons and things; as, John, Mary, Bos- 
ton, Washington, etc. Each of these objects has its parti- 
cular or proper name ; and hence such nouns may be called 
proper nouns. 

Lead the pupil to see also that many similar objects have 
a name in common; that the term /?07\se, for instance, does 
not distinguish any particular horse, but is a term common to 
all horses ; and that it may therefore be called a common 
noun. Lead them in the same way, when it is desirable, to 
the abstract and collective noun, and also to the classification 
in respect to form, — Simple, Derivative, and Compound. 

Classes of Verbs. — Verbs maybe classified in two ways: 
L With respect to their object, as Transitive and Intransitive ; 



258 METHODS OF TEACHING. 

2. With respect to their form, as Regular and Irregular. The 
old classification into active, passive, and neuter, is being dis- 
carded b}^ modern grammarians. It might be well to retain 
the term neuter for the verb to be, and regard other verbs as 
active and passive, instead of distinguishing them by voice. 
The passive verb seems a little simpler to the learner than 
the passive voice of the transitive verb. All active verbs do 
not express action, neither do verbs in the active voice. 

Transitive and Intransitive. — To teach the distinction of 
transitive and intransitive, lead the pupil to see, by examples 
and questions, that sometimes the action of the verb 2^(i'Sses 
over to an object, and sometimes it does not ; and that there 
are thus two kinds of verbs. Next lead them to see that the 
verb in which the action />a.sse.s over or makes a transition to 
the object may be called a transition or transitive verb, and 
that the others may be called intransitive. Then drill them on 
transitive and intransitive verbs, as found in sentences, and 
also in constructing sentences. 

Pupils should also be led to see that this distinction of tran- 
sitive and intransitive is not an absolute one, but that many 
verbs are used in both ways. Indeed, there is hardly a tran- 
sitive verb in the language that may not be used intransitivel3% 

Regular and Irregular. — To teach the distinction between 
regular and irregular verbs, lead the pupil to see that some 
verbs form the past tense hy adding ed, and others have no 
regular way of forming it, and that those which form it regu- 
larly may be called regular verbs, and that those which form 
it irregularly may be called irregular verbs. 

Pupils should then be drilled on the regular and irregular 
verbs. A list of the irregular verbs should be presented and 
carefully studied until the pupil is familiar with their proper 
forms. Sentences should be constructed requiring the use of 
the verb; and sentences erroneous in this respect, corrected. 
Verbs in the use of which there are frequent errors, as lay, 
lie, sit, sat, prove, di'vik, etc., should l)e carefull}- considered. 



TEACHING EXtiLISH GRAMMAR. 259 

Infinitii^es. — There are two forms dei'ived from the verb, 
usually called the infinitive mode and the jyarticiple. to which 
attention is briefly called. These ma}^ be taught hy the form, 
arbitrarily giving: them the names apj^lied to them ; or the}'' 
may be taught by their jase and meaning. The pupil may be 
led to see that the participle par^zcipafes in the nature of a A'erb 
and adjective, and is thus appropriately called a jyarticiple. It 
may also be shown that the infinitive, as to go, having no 
nominative, is unlimited by person and number, and is thus 
indefinite in this respect, and ma}' consequently be called an 
infinitive, which means unlimited. It maj" also be shown that 
the participle is also unlimited in person and number, and is 
thus also an infinitive; and that consequently there are two 
infinitives, the verb infinitive and the participle infinitive. 
The pupil should also be led to see that there are two partici- 
ples, the loresent and the past or passive. 

Classes of Pronouns. — Pronouns may be divided into five 
distinct classes ; Personal, Relative, Interrogative, Respon- 
sive, and Adjective. Authors are not fully agreed in this 
matter, but the classification given is convenient and as cor- 
rect as any we have noticed. 

Personal Pronouns. — In teaching Personal Pronouns, the 
teacher will lead the pupil to see that each one of these indi- 
cates by its form whether it is first, second, or third person, 
and may for this reason be appropriately called personal pro- 
nouns. A list of these should then be given, and the pupil 
maj/ be required to commit them to memory. The student- 
teacher may present an inductive lesson on the subject. 

Belative Pronouns. — A Relative Pronoun may be taught in 
two ways ; etymologically or logically. By the first method, 
we would show that it is a pronoun, because it stands for a 
noun ; and that it is a relative pronoun, because it refers 
hack or relates to some noun already named. The personal 
pronoun can be used independentl}^ of the noun ; but the rela- 
tive pronoun is always used in relation to a given noun. 



260 METHODS OF TEACHING. 

By the logical method we would teach that it is a pronoun 
as before ; and then lead tlie pupil to see that it is a relative 
pronoun, because it connects or relates the clause which it in- 
troduces to some previous word or clause. It will be well for 
the student-teacher to put both methods into an inductive 
lesson. The other classes of pronouns may also be easily 
taught in a similar manner. 

IV. Elements of Parsing. — The pupil should begin to 
parse as sopn as he begins grammar. As he learns each part 
of speech, he should be required to point it out in sentences. 
When he has learned some of the properties, he should also 
be required to give them in connection with the parts of 
speech. This is the kind of parsing that should be required 
in the Primary Course. It should be informal, and often con- 
sist merely of the answering of questions which the teacher 
may ask on the parts of speech and their properties. There 
should be no formal parsing, that is, no models should be fol- 
lowed which burden the memory with details. The main 
object should be to teach grammatical ideas and relations, and 
not grammatical forms of expression. To introduce these 
forms of parsing too eai'ly, is to burden the mind with forms, 
and thus prevent it from looking at the grammatical relations 
of words. 

Y. Elements op Analysis. — In this Primary Course, there 
should also be some instruction in the elements of grammat- 
ical analysis. This instruction should be presented as a gen- 
eralization of the offices of the parts of speech. Pupils should 
first be led to understand the subject and ■predicate oi the 
sentence. This may be done hy showing that the verb, which 
primarily was regarded as expressing action, is used in ex- 
presshig an assertion^ that the word in the nominative case is 
the subject of this assertion, and may be called the subject of 
the sentence, and that what is asserted is the predicate. It 
may then be shown that a collection of words may be used as 
the subject, and a collection of words as tlie predicate 



TEACIIIXQ ENGLISH GRAMMAR. 261 

We should pass next to the subordinate elements of the 
sentence. The pupil jnaj^ be led to see that the adjectives 
which originally were" regarded as expressing qualities, mark 
out or limit the meaning of nouns, and may be called limiting 
words. We should then pass from a single word as limiting a 
noun to see that a phrase and a clause may be used in the 
same manner, and may then also be regarded as limiting 
elements. In the same way the pupil may be led to see that 
the phrase and clause may also perform the office of an 
adverb, etc. 

The aim of this instruction is to teach the ideas of anal3^sis, 
and lead the pupils to see and understand these logical rela- 
tions ; but no formal analysis should be required of them. 
They may be required to answer questions and point out ele- 
ments ; but the}^ should not be required to commit and follow 
any set forms of statement, as is properly required of advanced 
pupils in grammar. 

YI. False Syntax. — Simple examples in False Syntax 
should be made use of from the beginning. Common errors 
in language should be presented, their faults pointed out and 
corrected. Mistakes heard on the playground should be 
brought in and corrected. Pupils should boi encouraged to 
watch their own language and to endeavor to correct all their 
mistakes. No formal methods of correction should be re- 
quired, however, as would be approi)riate for an advanced class. 

VII. The Logical Method. — After the pupil has attained a 
fair knowledge of the parts of speech, their properties, classi- 
fication, etc., with the elements of parsing and analysis, he is 
prepared to look at the subject of 'grammar from the stand- 
point of thought; and we should then introduce the elements 
of analysis b}^ what we have distinguished as the Logical 
Method of teaching grammar. 

In the Logical Method of teaching grammar, the sentence is 
made the basis of the instruction ; the method beginning with 
the logical analysis of the sentence. This logipal analysis, 



262 METHODS OF TEACHING. 

instead of being bnilt np b}^ a generalization from the nse of 
words, flows from the sentence as expressing a thought, and 
descends from the various elements as wholes to the parts of 
which tlie}^ are composed. The pupil is taught to look at a 
sentence as a logical whole, and to study the logical elements 
of which it is made up. Language is regarded as the expres- 
sion of thought, and the structure of language is determined 
by the laws of thought. 

The principles of Logic are thus to be made use of in deter- 
mining the principles of language. Words arc to be consid- 
ered not merely in their individual meaning, but as ex2:)ressing, 
individually and collectively, the logical relations of the ele- 
ments of thought. 

The subject and predicate are regarded as expressing con- 
ceptions of the mind, the one being compared with the other, 
and the sentence expressing the relation between them. In 
this they differ from nouns and verbs, which are usually re- 
garded not as expressing the mental product, but as the names 
of objects and actions. The subordinate elements are regarded 
as modifying elements, limiting the meaning or extent of the 
subject and predicate conceptions. In this they differ from 
the adjective and adverb etymologically considered, which 
express qualities of objects and actions.. The connective ele- 
ments are those which unite the other elements into a unity 
of structure. 

Method of Teachhif/. — In teaching by the logical method, 
we should begin by giving pupils a clear notion of an idea and 
a thought, and also of a sentence, as expressing a thought. 
We should then lead thefn to see that some ideas ai-e pa.)-- 
tioular and others are general, and that these general ideas 
embrace many individuals. We should then lead them to see 
how these general ideas are limited in their extent by other 
elements which, in comparison with the principal elements, 
may be called subordinafe elements. We should then teach 
them to see tlie ditfei-ent classes of subordinate elements, etc. 



TEACHING ENGLISH GRAMMAR. 263 

An Idea. — We may lead pupils to a knowledge of an Idea 
by having tliera look at an object, then think of the object 
when not looking at it, noticing the product in the mind, and 
telling them that this mental product is called an idea. The 
exercise we suggest is as follows : 

Model Lesson.— Teacher. Look at this book. Can you think of this 
book when j'ou do not see it ? Can you imagine you see this book when 
your eyes are closed? Do you seem to have a picture of it in your 
mind? Such a mental picture is called an Idea.- What then is the dif- 
ference between an object and an idea? Is the object in the mind? Is 
the idea in the mind? Where is the object? Pupil. Outside the mind. 
T. Where is the idea? P. Within the mind. Let there be a drill also 
to show that there are general ideas and terms, and to show the differ- 
ence between general and particular ideas and names. 

A Thought. — In order to teach a Thought, have the pupils 
form two ideas, compare them, and think the relation between 
them. This mental product, in which one idea is affirmed of 
another, is called a thought. The lesson is somewhat as 
follows : 

Model Lesson.— Teacher . Think of something, as a robin ; the menUil 
product is what? Pupil. An idea. T. Think of something else, as a 
bird; the mental product is what? P. An idea. T. Can you think of 
any relation between these ideas? can you unite them in any way? P. 
Yes, sir, — a robin is a bird. T. This mental product is called a thought. 
A thought is the relation of two ideas in such a way that one is asserted 
of the other. T. Compare the two ideas, a horse, and an animal, and 
affirm the one of the other. P. A horse is an animal. T. This is also a 
thought. What is the difference between an idea and a thought? How 
many ideas are necessary to a thought ? 

The Sentence. — In teaching a sentence, we merely show 
that it is the expression of the thought, either in .oral or 
written words. Take one idea or object of thought, and affirm 
some other idea or object of thought of the former ; write the 
expression on the board ; this will be a sentence. Be careful 
that the pupil sees that such combinations as sweet apjjles, 
etc, are not sentences. Teach also the difierent kinds of sen- 
tences. The student-teacher may give the lesson. 



264: METHODS OF TEACHING. 

Subject and Predicate. — To teach the Subject and Predicate, 
take a sentence, call attention to the two parts, showing that 
one is the name of that about which something is asserted, 
and the other is the name of that which is asserted ; lead them 
to call ihe first the subject^ from the subject of a composition; 
and the latter predicate, because the teacher saj'S that is its 
name. 

Model Lesson. — Teacher. In the sentence, Boys run, how many parts 
are there ? Which is the part about which something is said? Which 
is the part that tells what is said of boys ? Let us see what we sliall call 
these parts. When j'ou write a composition, what do you call that about 
which you write ? Pupil. The Subject of the composition. T. Very 
well; what shall we call boys, about which something is said in the sen- 
tence, boys run ? P. The subject of the sentence. T. What then is the 
subject of a sent jnce? The word rw/is does what? P. Tells or asserts 
something of boys. T. What may it be called ? P. The telling or as- 
serting word. T. Well, suppose predicate means the same as asserting 
word, what shall we call runs ? P. The predicate, etc. 

Subordinate Elements. — The Subordinate Elements may be 
taught somewhat as follows : Take a sentence like the follow- 
ing; " Man}' bright flowers ftxde quickly," and have them show 
what words can be omitted and still have a sentence; and 
lead them to call the necessary words, ^ow;e?*s and/aJe, being- 
more important than the others, the principal elements. The 
words many, bright, and quickly, being less important, are 
subordinate in rank, and may be called subordinate elements.- 
Lot the student-teacher give this in a lesson. 

Limiting Elements. — The next step is to teach that a sub- 
ordinate element limits the meaning or extent of the principal 
elements. This is peculiar to the logical method of teaching 
grammar, for by the etymological method, the adjectives ex- 
press the quality of the objects, and the adverbs the quality of 
the actions. In order to develop the idea of limitation, use 
the subject first in its full meaning, theu unite a word with it 
that restricts or limits it to a portion of its full meaning, and 
lead the pupil to see that the office of a subordinate element 






TEACHING ENGLISH GRAMMAR. 265 

is to diminish, or restrict, or limit the meaning of the general 
idea or term. 

Model Lesson. — Teacher. Wlien I say, "Girls study," how many girls 
may I mean? Pupil. All girls, or any number of girls. T. Suppose I 
say, "Good girls study," do I mean all girls? P. No, sir, only a part 
of girls. T Whkt word is it that restricts or limits the meaning of girls 
to only a part of girls ? P. The word good. T. What kind of an ele- 
ment may I call good which limits the meaning of girls? P. A limiting 
element. T. When I say, "Good girls study," do I mean any particular 
stud3'ing? P. No, sir. T. When I say, "Good girls study hard," do I 
mean any particular kind of studying? P. Yes, sir, Jiard studying. 
T. "What word limits the meaning of study to hard studying? P. The 
word hard. T. What kind of an element then is hard ? P. A limiting 
element. 

Kinds of Subordinate Elements. — The different kinds of 
subordinate elements are ivords, phrases, and clauses. These 
may be taught by taking an example in which a single word 
limits tlie subject, then a phrase expressing the same thing, 
and then expressing the same with a clause. 

Model Lesson. — Teacher, writing on the board, "Normal girls study 
diligently," says. What word limits or tells the kind of girls? P. The 
word JS'ormal. T. Suppose I write, "Girls of tlie Normal study dili- 
gently," what now expresses the kind of girls? P. The words of the 
Normal. T. Such a collection of words is called a phrase. Suppose I 
write, "Girls who live at the Normal study," etc., what nowtells the kind 
of girls? P. Tlie words if/io live at the Normal. T. Is there a subject 
or predicate in this expression, "who live at the Normal V Is it then a 
sentence? Such a limiting expression is called a clause. What kind of 
words limit nouns? P. Adjectives. T. What do these three kinds of 
elements limit? P. They limit nouns. T. What kinds of elements then 
may we call them? P. Adjective elements. T. How many kinds of «d- 
jectice elements tlien are there ? P. Three— ?rorf/s, phrases, and clauses. 
In a similar manner, the adverbial elements may be presented, and also 
the objective elements. The student-teacher should give the lesson. 

In presenting the limiting element, we have regarded it as 
liviiting the application of the general term: we may also 
present it as limiting the extent of the concept. The former 
method is in accordance with Nominalism ; the latter with 
Conceptualism. 



266 METHODS OF TEACHING. 



IV. Methods of Teaching Advanced Grammar. 

After the pupils have attained a fair knowledge of the parts 
of speech, their properties and .classification,' "with the ele- 
ments of parsing and analysis, they are prepared to take up 
the subject of grammar in a more thorough and scientific 
manner. They are then prepared to consider the minutiae and 
more difficult points of the subject, to present their knowledge 
in a complete and systematic form, to discuss the idioms of 
S3aitax, to learn and apply the rules of construction, and see 
the logical relation of the elements of language as determined 
by the processes of thought. This higher course should in- 
clude a continuation of the etymological exercises of the pri- 
mary course, the committing of the principal definitions of the 
science, a full course in parsing and correcting false S3'ntax, 
a complete course in logical anal^'sis, and the grammatical 
analysis of some of the masterpieces of the language. We 
shall speak of this course under the several heads, the Study 
of the Text-book, Formal Parsing, Correcting False Sj'ntax, 
and Grammatical Analysis. 

I. Study op Text-book. — A text-book should now l)e placed 
in the hands of the pupils, and regular lessons assigned for 
them to prepare for recitation. The definitions, as given in 
the text-book, unless changed by the teacher, should be com- 
mitted and recited verbatim, care being taken that they are 
understood. The notes and observations should be carefully 
studied, and their sense, not the exact words, be required to 
be given in the recitation. 

The pupils should be drilled in declensions, comparisons, 
and conjugations, until they can run through these exercises 
with rapidity and accuracy. They should also be drilled on 
the classification of the parts of speech, and be required to 
write logical outlines of the same. 

In the primary course, the instruction was Inductive ; in 



TEACHING ENGLISH GRAMMAR. 267 

advanced grammai' it should be deductive. There, the effort 
was to lead the pupil to understand the ideas ; here, it is as- 
sumed that the pupil nlreudy understands the leading princi- 
ples, and is able to acquire other ideas and to recite them. 
Of course, an}' subject not understood should be explained, 
inductively or deductively, as the teacher ma^' prefer. 

The Rules should be committed to memory by their num- 
bers, so that they may be readily referred to in parsing and 
correcting false syntax. Notes on the rules, showing their 
application to peculiar cases and also the exceptions to them, 
should be thoroughly studied. Pupils should be drilled in 
the peculiar use of words, the idioms. of construction should 
be explained, and all the more difficult parts of grammar con- 
sidered. It is also suggested that the more important sub- 
jects be taken the first time of going through the book, leav- 
ing the details to be learned on the review. The course, if 
there is time, should reach up also into the philosophical 
principles of the subject, and embi'ace the laws of universal 
grammar. 

II. FoRMAi Parsing.; — In connection with the study of the 
subject in the text-book, there should be regular exercises in 
Parsing. This is an old exercise, which modern analysis has 
to some extent thrown into the background; but it is of great 
value, and should not be neglected in grammatical instruction. 

Nature of Parshifj. — Parsing consists in naming the differ- 
ent parts of speech in a sentence, their classes, properties, and 
relations. It is a consideration of the grammatical use of 
words in sentences. Parsing may also be defined as the 
grammatical description of words in sentences. The term is 
derived from pars, a part. It is an exercise that should be 
begun as soon as the pupil has learned a few of the elementary 
ideas of grammar, and should be continued through the entire 
course of advanced grammar. 

The object of parsing is two-fold. First, it affords an op- 
portunity to apply the definitions, classifications, and proper- 



268 METHODS OF TEACHING. 

ties which have been learned. It thus aids the pupils in 
becoraiug familiar with the definitions and rules of grammar, 
by frequent repetition ; and teaches them to ex})ress their 
knowledge in a systematic manner. Second, it requires pupils 
to examine language and ascertain the nature and relation of 
words in sentences ; and this not only gives power in the 
analysis of language, but cultivates the habit of abstract 
thought. The object of parsing should be distinctly under- 
stood, for teachers too often have acted as if the end of study- 
ing grammar is to learn to parse ; and their pupils were drilled 
upon the exercises until they could, with propriety, be called 
" parsing machines." 

For exercises in parsing, we should first use the sentences 
given in the text-books. As the pupils advance, we should 
introduce some other work containing good specimens of 
English literature. The school reader may be conveniently 
used as a "parsing book." A little work, i:)repared by 
Rickard and Orcutt, called Class-book of Prose and Foeiry, is 
also recommended. Many of the older teachers of grammar 
used such works as Thomson's Seasons, Milton's Pai-adise 
Lost^ Pollok's Course of Time, Cowper's Task, Pope's Essay 
on Man, etc. ; and they are still recommended to teachers of 
advanced classes. 

Forms of Parsing. — In parsing, beginners should not be 
required to use complete and logical forms. It is best for 
them to go over the words, point out the j^arts of speech, and 
name such properties as they have studied, and then answer 
such questions as may be asked by the teacher. The objec- 
tion to using forms of jjarsing with beginners is, that pupils 
will be thinking more about the form than the grammar; and 
will fall into a dull routine of words instead of thinking of the 
grammatical relations. Forms of parsing should not be intro- 
duced until the pupil is quite familiar with the fundamental 
ideas of grammar. 

In the advanced course, however, pupils should be required 



TEACHING ENGLISH GRAMMAR. 269 

to use a, definite scheme of statement, which vre call Forms of 
Parsing. Such Forms are needed for several reasons. First 
they economize time by requiring the pupils to tell what thcj 
know in a simple, direct, and unhesitating manner. Second, 
they facilitate criticism, as we can v.er3^ much more readily 
detect and remember a mistake when the pupil has a regular 
order of statement, than when he mentions the properties and 
relations in a haphazard sort of wa3\ 

The forms of parsing should be simple. The complicated 
forms which we sometimes meet with, are a positiA'e disadvan- 
tage and hindrance to the pupil. The form is often so com- 
plex and difficult that it requii-es nearly all the mental energy 
of the learner to follow it, and leaves but little for the grammar 
proper. Pupils often make mistakes in parsing, not because 
they do not understand the grammatical relations, but because 
some part of the form slipped from the memory. Most of the 
corrections made in the class-room, in a parsing lesson, it is 
often noticed, are with respect to omissions or variations of 
the adopted form. 

No expressions should be used in the forms that are not 
clearly understood by the pupils. A violation of this rule is 
a very common error. Nine-tenths of those who use such 
expressions as "prepositions govern the objective case," "ad- 
jectives relate to nouns," " adjectives limit the nouns to 
which they belong," "adverbs qualify or modify verbs, adjec- 
tives, and other adverbs," use them without any definite idea 
of their meaning. If such expressions are used, require the 
pupils to see clearly what is meant by "govern,." " relate to," 
"qualif}''," " limit," "modify-," etc. It is said that a pupil, on 
being asked something about the expression " grammatical 
persons," as used by an author in defining personal pronouns, 
replied by naming the three principal grammar teachers of 
the institution. 

The full form of parsing should often be dispensed with. 
When the pupils are familiar with the form, it is a waste of 



270 METHODS OF TEACHING. 

time and patience to have them repeat the same "lingo" day 
after day. Let a portion of tlie time be spent in having them 
point out tlie i-elations of words and answer questions upon 
some of the more important and difficult things connected, 
with the sentence. Thig will teach them to think grammar, 
and not merel}' to repeat foj'mulas. 

In parsing, we should generally jDroceed from word to word 
in the order of their arrangement in the sentence. Frequently, 
however, the teacher may select the words to be parsed, as it 
is often a waste of time to parse all the familiar words. The 
neglect of this is a common error in teaching grammar. We 
may also have an exei'cise in which the pupils are required to 
parse all the nouns in a paragraph, then all the verbs, then all 
the- adjectives, etc., in their order. 

• Oral JParsiitf/. — We shall now present a form of Ot^al 
Parsing. Let the sentence be, " The man who came j'ester- 
day gave me a pair of beautiful sleeve-buttons." The form of 
parsing is as follows : 

The is the definite article; it limits man. Rule. 

Man is a common noun; in the masculine gender, third person, and 
singular number; it is used as the subject of gave, hence it is in the 
nominative case. Rule. 

Who is a relative pronoun; its antecedent is man, hence it is in the 
masculine gender, third person, and singular number. Rule. It is used 
as tlie subject of carne, hence it is in the nominative case. Rule. It 
intro luces the clause, -who came yesterday, and joins it to man. Rule. 

Came is an irregular, intransitive verb; principal parts, come, came, 
coming, come; it is in the indicative mode, and past tense; its subject is 
who, hence it is in the tliird person and singular number. Rule. 

Yesterday is an adverb of time; it modifies came. Rule. 

Gave is an irregular, transitive vex'b; principal parts, give, gave, giving, 
given; it is in the active voice, indicative mode, and past tense; its sub- 
ject is man, hence it is in the third person and singular number. Rule. 

Me is a perir'ohal pronoun; in the common gender, first person, and sin- 
gular number; it is the object of the preposition to understood, hence it 
is in the objective case. Rule. 

A is the indefinite article; it hmitspair. Rule. 



TEACHING ENGLISH GRAMMAR. 



271 



Pair is a common noun; in the neuter gender, third person, and sin- 
gular number; it is the object of gave, heace it is in the objective case. 
Rule. 

Of is a preposition; it shows the relation of sleeve-buttons to pair. Rule. 

Beautiful is a descriptive adjective, in the positive degree; it modifies 
sleeve-buttom. Rule. 

Sleeve-buttons \s a. compound common noun; in the neuter gender, third 
person, and plural number; it is the object of o/, heuce it is in the object- 
ive case. Rule. 

Written, Parsing. — There should be forms of Written 
Parsing, as Avell as of Oral Parsing. There are several advan- 
tages in written parsing. First, it enables all the class to 
be reciting at the same time. Second, it Impresses the rela- 
tions of Avords by seeing them written. Third, it leads to an 
exactness of statement that the oral method does not always 
attain. This written parsing can be on the blackboard or on 
paper. The oral and wi'itten methods can be combined in the 
same recitation to great advantage. 

We present also a form of written parsing, using the sen- 
tence given below. The sentence is first written on the 
blackboard or paper, a line is drawn under it, and the words 
are parsed as shown in the form. If too long for the space 
assigned, the sentence may be divided as in ordinary writing, 
room being left between the parts of the sentence for parsing 
the words. 

yesterday! gave 
at I i tv 
came ' give 
gave 
giving 
given 
a 
i 
pa 
man 
3 
s 

It is thought that the abbreviations used explain them- 
selves. If they do not, a reference to the forms of oral pars- 



The 


man 


who 


came 


da 


en 


rp 


i i V 


man 


m 


man 


come 


3 


m 


came 


■s 


3 


coming 


gave 


s 


come 


n 


came 


i 


n 

man 


pa 
who 


3 1 








s 1 



me 


a 


pair 


of 


PP 


la 


en 


P 


c 


pair 


n 


pair 


1 


3 




s 


s 




(to) 


gave 




o 










bracelets. 

en 
n 
3 

P 

gave 

o 



272 METHODS OF TEACHING. 

ing will make them clear. For a fuller presentation of the 
subject, see Forms of Parsing and Analysis, b}"- Prof. E. 0. 
Lyte. 

Errors in Parsing. — Errors in Parsing consist of three 
classes; first, errors in stating the part of speech to which a 
word belongs, its properties, construction, etc.; second, errors 
of expression ; third, errors in the form of parsing. Some of 
these errors are the result of a want of knowledge on the part 
of the pupil, some arise from carelessness, and others are due 
to the adoption of incorrect forms on the part of the teacher. 

Errors of expression Include the mispronouncing of words, 
such as "nomitive" for "nominatiAe," "singlar" for "singu- 
lar," etc.; the improper omission or contraction of words, 
such as, " John 's a proper noun" for " John is a proper noun ;" 
the use of ungrammatical or awkward expressions, such as 
" nominatiA'^e case, subject of is," " nominative case governs 
the verb," etc. 

The forms of parsing used by many teachers and presented 
in some of our text-books, contain expressions which are 
awkward. We call attention to a few of these expressions, 
suggesting that teachers be especially careful in a grammar 
recitation to teach correctness and elegance of expression. 

Thus, '■'■John is a noun^projyer,'' is as awkward as "John is a 
mail, aged," which no one would use in natural expression. 
Again, we often hear, '■'■John is a noun, 2^'>'oper, masculine 
gender;''^ which really saj^s that John is projjer, is masculine 
gender. This is of course incorrect, as it is not John that is 
proper, but the noun John. 

Pupils often use the expression, *^ according to rule.^^ This 
is too general an expression ; a carpenter builds a house " ac- 
cording to rule," etc. We should say, "according to Rule 1," 
etc.; or, ** according to the rule," keeping the voice suspended, 
and repeating the rule. 

Pupils often have the habit of using the word and immedi- 
ately after naming the part of speech ; as, " The is an article, 



TEACHING ENGLISH GRAMMAR. 273 

and belongs," etc. "Q/is a preposition, and shows the rela- 
tion," etc. In these cases there are two distinct thoughts, the 
second not being a continuation of the tirst, and therefore not 
to be coupled with it. We should not say, "Mary is a girl 
and studies her lesson," but " Mary is a girl; she studies her 
lesson." In the same way it is better to say, " The is an arti- 
cle ; it belongs," etc. 

Pupils often use the expressions, " Third person, it is spoken 
of," " Second person, it is spoken to," etc., thus confounding 
the noun which they are parsing with the person or thing 
denoted by the noun. " Third person, it denotes the person 
spoken of," "Second person, it denotes the person spoken 
to," etc., are better forms. The teacher should correct these 
and other errors which he meets in parsing, for the language 
used in reciting grammar should be grammatical. 

III. Grammatical Analysis. — Within a comparatively 
short period of time, there has been introduced into grammar 
a logical method of considering the sentence, which has re- 
ceived the name o^ grammatical analysis. It has done much 
to improve the study, and is regarded as of great importance 
in a system of grammatical instruction. 

Nature of Analysis. — In the etymological stud}' of gram- 
mar, words are considered as parts of" speech, and classified 
into nouns, verbs, etc. These individual words perform cer- 
tain offices in the construction of sentences and receive their 
naines from the offices which they perform. By and by it is 
observed that collections of words have an office in sentences 
similar to man}^ of the parts of speech. It is also seen that 
all sentences may be regarded as consisting of two principal 
elements, several subordinate or modifying elements, and 
several connective elements. The discussion of a sentence 
with respect to all these elements has been called Grammatical 
A nalysis. 

The Elements. — Grammatical Analj^sis regards the sentence 
as consisting of three classes of elements ; the principal ele- 
12* 



274 ■ METHODS OF TEACHING. 

merits, the svhordinate elements, and the connective elements. 
The principal elements are the subject and predicate ; the sub- 
ordinate elements are the adjective, the adverbial, and object- 
ive elements ; the connective elements include the prepositio7i, 
the conjunction, the relative pronoun, etc. Besides these, 
there is sometimes an element having no relation to the other 
elements, called an independent element. All sentences are 
regarded as composed of these elements, which elements ma}'- 
be represented by individual words, or by collections of 
words. 

Importance of Analysis. — The importance of grammatical 
analysis in the study of language can hardly be overstated. 
It gives one an insight into the principles of the structure of a 
sentence tliat can be obtained in no othei* way. It lifts the sub- 
ject up into the domain of logic, and enables one to examine 
the sentence in the light of those forms of thought which give 
rise and shape to the sentence. It enables one to see some of 
the functions, of the parts of speech that do not appear in the 
etj'mological study of words. Thus, the full office of arelative 
pronoun cannot be appreciated until we see that it joins a 
restrictive clause to some word, and the idea of a restrictive 
clause is given by analysis. S® also the antecedent term of 
the relation of a preposition is not always evident until we 
see the relation of the modifying phrase which it introduces, 

Analj'sis thus becomes a powerful instrument in the hands 
of the grammarian for understanding the grammatical rela- 
tions of language. Some writers go so far as to sa^y that 
"grammar can be successfully studied in no other wa}'." 
Dr. Wickersham says that " parsing without a preceding 
anal^^sis can lead to but a very imperfect knowledge of the 
organic structure of sentences." Prof. Whitney remarks, 
" Give me a man who can, with full intelligence, take to pieces 
an English sentence, brief and not too complicated, even, and 
I will welcome him as better prepared for further study in 
other languages than if he had read both Ceesar and Yirgil, 



TEACHING ENGLISH GRAMMAR. 275 

and could parse them in the routine style in which they are 
often parsed." 

Order of Parsing and Analysis. — The order of instruc- 
tion in grammatical analysis and etymological parsing is a sub- 
ject upon which authors are not agreed. The old method was 
to begin with the study of words; and, after quite a full knowl- 
edge of their etymological properties, to pass to the analysis 
of sentences. A large number of recent writers maintain that 
we should begin with the sentence and present the logical ele- 
ments before we teach the parts of speech, " Since the gen- 
er-al precedes the sjjecial.,^' says one writer, " the treatment of 
sentential analysis should precede any exercises in parsing." 
Several grammarians endeavor to construct their text-books 
on this principle ; but most of them drop unconsciously into 
the etymological consideration of words befoi'e presenting 
their logical use. 

It is our opinion that grammatical analysis should follow 
the etymological consideration of words. There are seA'eral 
reasons for this opinion. First, the logical elements used in 
analysis are really a generalization of the uses of the parts of 
speech. Grammatical analysis was really the outgrowth of 
grammatical parsing, by a generalization :of the etymological 
uses of words. Thus, we should understand the use of a ivord 
as an adjective before we are able to see clearl}' the adjective 
use of a jjhrase or a clause. It thus follows the order from the 
particular to the general, which is the correct order for primary 
instruction. This was also the historic order — parsing was in 
use a long time before grammatical analysis was thouglvt of — 
and the historic order often indicates the order of teaching. 

It is also much easier to begin with the etj^mological method. 
A pupil will find it very difficult to understand the use of the 
logical elements before he is familiar with the use of words as 
parts of speech. An adjective or adverbial element will hardly 
have any meaning before the pupil is familiar with the adjec- 
tive and adverb. The idea of limitation, which is the analyt- 



276 METHODS OF TEACHING. 

ical idea of an adjective and adverbial element, is much more 
diflScult for a beginner th'an the etymological idea of adjec- 
tives as expressing qualities of objects and adverbs as ex- 
pressing f7^<aZ^Y^es of actions. The very nomenclature in log- 
ical analysis is derived from the use of words as parts of 
speech. It is thus evident that sj-ntactical parsing and the 
knowledge it implies, should precede the study of grammatical 
ajialj'sis. 

How Teach Analysis. — Logical analysis is thus best 
taught to beginners b}^ a generalisation from the nature and 
use of the parts of speech. Thus it may be seen that the 
noun, which was primarily a name, is often the subject of an 
assertion, and that the verb, which was primarily an action- 
word, is used to assert or predicate something of the subject 
It ma}^ then be shown that several words may express the 
subject of the assertion, and also that several words may 
express the predication. Again, it may be seen that the 
adjective, which expresses primarily a quality of an object, 
may be used to limit the meaning of the noun, and also that 
the adverb may limit the meaning of a verb ; and rising from 
this idea, we may see that a collection of words may perform 
the office of an adjective or an adverb, and thus become a 
limiting element. In this way the learner may reach a clear 
idea of the logical elements of sentences. 

It is recommended that the elements of analysis be pre- 
sented as early in the course as pupils are prepared to under- 
stand it. After the pupil is familiar with the parts of speech 
and their general offices, he may be led to the idea of a subject 
and a predicate, and to see that collections of woi'ds perform 
the same office in the construction of sentences as individual 
words. He may thus be led graduall}^ into the generalizations 
of grammatical analj'sis. 

At a certain stage of grammatical instruction it is recom- 
mended that the logical method of treating the sentence 
should be presented, the pupil being taught to look at the 



TEACHING ENGLISH GRAMMAR. 277 

structure of a sentence through the thought. This will give 
him additional power in the analysis of language, as it. enables 
him to look at the grammatical constructions through the 
medium of thought, which gave it existence and moulded it 
into its present form. 

He may be led to a clear idea of ideas^ of their comparison 
giving rise to judgments^ which expressed, give the proposi- 
tion ; and then learn to distinguish the subject and predi- 
cate of the proposition. He may then pass to the idea of the 
limitation of the extent of a concept, and thus of a limiting 
element; and see that these may consist of words, phrases, 
and clauses. In this way he can reach the details of analysis, 
passing down until it meets its complement, parsing, in the 
etymological use of the individual words of which a sentence 
is composed. 

This logical analysis may be presented less subjectively by 
regarding the ivords as denoting objects, classes, etc., in- 
stead of ideas; and the subordinate elements as pointing out 
or distinguishing particular individuals or classes, instead of 
limiting the ideas; or as limiting the application of the term 
rather than limiting the idea or concept. This latter method 
is more objective than the former and probably a little sim- 
pler; but it does not seem so closely related to the laws of 
thought as the logical method previously described. It would 
no doubt be more acceptable to the "nominalist" than the 
former method. 

Methods of Ana li/ sis. — The logical analysis of a sentence 
may be presented in two distinct ways, which may be distin- 
guished as the analytic and synthetic forms. By the former 
method, we first name the sentence as a whole, then separate 
it into its parts, naming the entire subject and the entire 
yn'edicate, then pass from the entire subject to the simple or 
grammatical subject, and name its limitations, and proceed 
to an analysis of each of those elements ; and then analyze the 
predicate in the same manner. 



278 METHODS OF TEACHING. 

B}^ the other method, we first name the sentence as a 
whole, then name the simple subject, then the subordinate 
elements which limit it, giving an analysis of these subordi- 
nate elements, then put the simple subject and its subordinate 
elements together and name the complete or logical subject ; 
and then proceed in the same manner with the predicate, 
passing from the simple to the entire or logical predicate. 

These two methods are very nearly opposite in form, though 
they do not differ in spirit. Some teachers prefer one method 
and some the other, though it is diflicult to tell which is 
preferable. The synthetic is probably a little easier, as it 
gives a little more time to see what the full subject or predi- 
cate of the assertion is. It should be noticed that the syn- 
thetic form of statement is just as much an exercise in logical 
analysis as the analytic method ; the spirit is the same, the 
only difference is in the form or order of statement. 

Forms of Analysis — We shall now present some forms 
for oral and written anal^^sis. The necessity of such forms 
is clear from what has been said in regard to forms for oral 
and written parsing. The forms for analysis should possess 
the same attributes as those for parsing ; that is, they should 
be simple, clear, and logical. The forms presented are nearly 
the same as those used by Prof. L3'te in his Forms of Parsing 
and Analysis. To illustrate, we take the sentence used to 
represent the forms of parsing, — " The man who came j'ester- 
day, gave me a pair of beautiful sleeve-buttons." 

Oral Analysis. — This is a complex declarative sentence. Man is the 
subject; it is limited by the, an article, and icho came yesterday, an ad- 
jective clause; w/io is the subject of the clause ; it is used also as a 
subordinate connective ; came is the predicate ; it is limited by yes- 
terday, an adverb. Gave is the predicate of the sentence ; It is limited 
by to me, an adverbial phrase ; to, understood, is a preposition, connect- 
ing gave and me ; me is the object of to; gave is also limited hy pair, its 
object ; pair is limited by a, an article, and of sleeve-buttons, an adject- 
ive phrase ; of connects pair and sleeve-buttons ; sleeve-buttons is limited 
by beautiful, an adjective. 



TEACHING ENGLISH GRAMMAR. 279 

WRITTEN ANALYSIS, OR OUTLINE. 



man 


'" 




The "'■' 


adj 


who * " 




came p 




yesterday "^ 


gave 


p 




(to)P me" 




adv 




pair" 




^an 




of^ sleeve-bnttons" 



'"'■^' beautifully 

Some teachers prefer a slightly different method of stating 
the analysis. Thus, instead of saying, " it is limited by who 
came yesterday^ an adjective clause," they say, " it is limited 
by loho came ye^tet^day, a clause used as an adjective." Still 
another method is, " it is limited b}"" the adjective clause who 
came yesterday,^' which we like about as well as the model we 
have given. It is a question whether we should name the parts 
of speech in analysis; thus, whether we should say, "it is lim- 
ited by the, an article," or rather, "it is limited b}' the, an ad- 
jecth'e element," or "by the adjective element ^7ie." Logical 
analysis may be complete without mentioning or even knowing 
the parts of speech ; though it is convenient to use the name 
of the part of speech when the element is a single word. 

Mixed 3Iethod. — There is also a method of disposing of 
sentences that combines analysis and an abridged method of 
parsing, which may be called a mixed method or graw.matical 
description. This is' a valuable practical method, and is re- 
commended for the use of pupils who are familiar with the 
el-'^ments of parsing and analysis. The method may be illus- 
trated with the sentence, " The man whom I saw yesterda}^ 
lives in Boston." We present it in two different forms; one 
b'^ing somewhat synthetic and the other somewhat analytic. 

First Form. — The man iDJioml saio yesterday lives in Boston. This is a 
f^omijlex, declarative sentence. The is an article ; it is used to modit/ 
man. Man is a noun; it is used as the subject of lives. Wlwm is a rela- 



280 METHODS OF TEACHING 



tive pronoun, its antecedent is man; it is used as the direct object 
saw; it introduces tlie clause wloom I saw and joins it to ma/i. Whoin 
I saw is a clause used as an adjective; it modifies man. /is a pronoun; it 
is used as the subject of saw. Saw is a verb; its subject is /. Yesterday 
is an adverb; it is used to modify saw. /is th? subject of the clause, and 
saw wJiom is the entire predicate. Lices is a verb; its subject is man. In, 
is a preposition; it is used to introduce tlie phrase in Boston, and join 
it to lives. In Boston is a phrase used as an adverb; it modifies lives. 
Boston is a noun; it is used as the object of in. Tlie man whom T saw 
yesterday is the entire subject of the sentence, and lives in Boston is 
the entire predicate. 

Second Form. — The man whom I saw lives in Boston, is a complex sen- 
tence. The man lives in Boston is the principal clause, and rclujm I saw 
is the subordinate clause. I'he man whom I saw is the entire subject; 
and lives in Boston is the entire predicate. Man is a noun used as subject 
of lives. Tlie is an aiticle, used to modify man. Whom I saw is a clause, 
usetl as an adjective to modify man. /isa pronoun, used as subject of saio. 
Saw is a predicate verb; its subject is /. Whom is a relative pi'onoun; as 
a pronoun it is used as object of saw, as a relative or subordinate connect- 
ive it introduces the clause whom I saw, and joins it to man. Lives isa 
predicate verb; its subject is man. In Boston is a phrase used as an 
adverb to modify lives. In is a preposition used to show the relation of 
Boston to lives. Boston is a noun used as the object of in. 

Errors in Analysis. — Errors in analysis consist of two 
classes: fii'St, errors in stating the classification and elements 
of a sentence; and second, errors of expression. Errors of 
expression include the misuse of terms, such as clause for 
phrase, sentence for clause, or member; the needless repeti- 
tion of terms, such as "of which," the use of unnecessarj' 
terms, such as "elements of the second class," " elements of 
the third class," etc. A very common error in forms of analy- 
sis is the use of long and involved sentences in which the 
thought becomes obscured in the construction. The different 
points should be simply and dii-ectly stated. 

In written analysis, the commonest errors are, — errors of 
arrangement, and errors in writing the abbreviations. The 
teacher will be careful to guard against the following mis- 
takes : Drawing the lines too long, or in an oblique direction ; 



7|i 

I 



TEACriINQ ENGLISH GRAMMAR. 281 

failing to write the modifying words and the connectives in 
tlie proper places ; writing the predicate too far below the sub- 
ject; failing to write the proper abbreviations in the right 
place, and in a smaller hand than that used in writing the 
sentences. 

Diuf/ranis for Analysis. — Several efforts have been made 
to devise some form of written analysis which will picture the 
grammatical relations to the eye. The most prominent of 
these methods is that of Prof. Clark, called the "diagrammat- 
ical method," given in Clark's grammar. A method of graphic 
anal3'sis that looks well upon the board is that given in. Reed 
and Kellogg's grammar. It is supposed that such a represent- 
ation aids the learner in grasping the grammatical relations 
of words, on the principle that the abstract idea may be seen 
througii the pictured form. The objection to some of these 
methods is that it often requires more ingenuity to prepare the 
diagram than to understand the grammatical relations. If 
used at all, they should not be made prominent, or a pupil will 
become so dependent upon them that he will be unable to see 
the grammar of a sentence except through the medium of a 
diagram. Used occasionally for illustration, they may be of 
value to the student ; but when employed as a regular method 
of recitation, we believe them to be objectionable. 

lY . Correcting False Syntax. — By False Syntax we mean 
constructions in language which violate the laws and usages 
of grammar. The principle upon which the correction of 
false syntax is based in teaching grammar, is that we learn 
the true b}' seeing the false ; as the Spartans taught their 
children temperance by showing them the silly actions of the 
Helots when intoxicated. 

The object of correcting false syntax is twofold. First, it 
gives a clearer knowledge of the rules of syntax, and th^'iir 
application to language ; second, it impresses the correct form 
of the sentence, and leads us to avoid the errors with which 
we are thus made familiar. Its importance in a course of 



282 METHODS OF TEACHING. 

grammatical instruction is thus apparent : it aids the pupils 
in obtaining a more thorough knowledge of the rules of gram- 
mar, and trains them to acquire correct habits in the use of 
language. 

The exercises selected should in the main be such as actu- 
ally occur in conversation and writing, and not all sorts of 
imjjossible errors. It is hardly worth while to manufacture 
errors such as may never be heard or seen in language, as 
enough actual mistakes may be found to illustrate ever}^ rule. 
The errors of common conversation should be made especially 
prominent, as " Please let John and I go home," " Who did 
you see," " Who were you with," etc. We should also have 
examples of the mistakes involving the nicer distinctions of 
gi"ammar, as the use of shall and will, the forms of the irreg- 
ular verbs, and the popular tendencies to depart from the strict 
rules of s^-ntax. The slips of eminent writers will be found 
useful to impress upon the minds of pupils the necessity of 
being careful in writing. 

The exercises in false sjmtax should be v>sed in connection 
with parsing and analysis. They ma}' be given along with the 
etymological exercises of the book after the correct forms have 
been explained. Some authors, as Goold Brown, give a large 
collection of such exercises under the detailed discussion of 
the rules of syntax, which is a very convenient method of con- 
sidering the subject. Some teachers recommend that the ex- 
ercises be graded, following the order of the sentence, proceed- 
ing from the simplest form of the sentence in the first step to 
the most complicated form in the last step ; but, though such 
a treatment would be logical, it is a question whether it would 
possess any practical value. 

Forms of Correcting. — With beginners, as already stated 
in the primary course, no special form is to be used in recita*- 
tion,the object being to call attention to the error and correct 
the practice. With the advanced course, some definite form 
should be used by the pupils in recitation. This form, as in 



TEACHING ENGLISH GRAMMAR. 283 

parsing and analj-sis, should be as simple as is consistent witli 
a clear and complete statement of the nature of the error and 
its correction. The teacher may have his pupils use a full 
form until they are familiar with it, and then pass to an 
abbreviated form. Frequently in the recitation, all form 
should be dispensed with, the pupil merely being required 
to state the error and the correction. We present several 
forms, as suggested by Prof. Byerly, and used by him in his 
classes. 

First Form. — The lirst method of correcting false syntax 
embraces five distinct things : 1. The pupil states that the 
sentence is incorrect ; 2. He shows wherein the rule is vio- 
lated ; 3. He quotes the rule violated as authority ; 4. He 
states what should be omitted, supplied, substituted, or 
changed ; 5. He gives the sentence in its correct form. To 
illustrate, take the sentence, " Who went ? Us girls." 

Illustration. — "Who went? Us girls." This sentence is incorrect; 
because "us," a pronoun in the objective case, is used as the subject of 
"went"; but according to Rule I., A noun or a pronoun used as the 
subject of a finite verb must be in the nominative case ; therefore, instead 
of "usj' "we" should be used; and the sentence should be, "Who 
went? We girls." 

Second Form Another method is that which gives the 

result first and the reason afterward. It ditfers from the first, 
as' the last two steps of that are made the second and third in 
this. We illustrate with the same sentence. 

llltistrndon.—" Wlio went f lis girls." This sentence is incorrect; 
instead of "us," " we" should be used ; and the sentence should be, — 
" Who went? We girls"; it is incorrect because "us," a pronoun used 
as the subject of "went" understood, is not in the nominative case ; but 
according to Rule I., etc. 

Other Fo7-ms. — Other methods, less formal than these, may 
also be used. Thus, we may name the error, then the correc- 
tion, and then give the reason for the correction b}' quoting 
the rule. Another form, which we should often use^ is that 



284 METHODS OF TEACHING. 

m which the pupil reads the sentence as given, and then 
simply reads it as corrected. 

Error's in Correctiiiff. — There are several erroneous ex- 
pressions to which pupils are liable in correcting false syntax, 
which should be avoided. First, the pupil should not be al- 
lowed to say " ' us' should be changed to ' we' ", as that cannot 
be done. Second, the pupil should not say " The sentence 
should read".; but rather "the sentence should be." 

Written Exercise. — There may also be a written exercise 
in correcting false syntax. The teacher may dictate the sen- 
tences and have them written on paper or on the blackboard, 
and then have them corrected by drawing a line under the 
incorrect word and writing the correct word below it. Or the 
teacher can write several sentences on the board, numbering 
them in the order in which they are written, and require the 
pupils to write them correctly, indicating them b}^ the proper 
numbers. When written on paper, they may be read or 
handed to tlae teaclier to look over out of class, and be re- 
turned at the next recitation. 

Some of the sentences assigned should be correct, some 
should contain an ei'ror to be corrected, and some should have 
introduced into them some error, easily detected, to hide, as 
it were, some other error not so easily observed. The teacher, 
of course, should inform the class that some of the sentences 
are correct, some contain one error, some two errors, etc'. It 
will be well to introduce all kinds of linguistic errors in these 
exercises. Thus the sentences presented may contain errors 
in spelling, in the use of capitals, in punctuation, in the use of 
words, etc. 

Exercises in false syntax are usually found in the text-book, 
and may be studied by the pupil before coming to the recita- 
tion. The teacher may also prej^are a list of such incorrect 
sentences as seem to him likel}"- to be used, and also of such 
as he has met with in his reading or has heard in the vicinity 
of the school. He should encourage his pupils to prepare a 



TEACHING ENGLISH GRAMMAR, 285 

list of incorrect sentences which they may hear used, and also 
to examine the books the}'^ are reading to see whether they can 
detect any errors in grammar. Such an exercise will make 
their grammatical sense very susceptible and accurate, and 
lead to great care in their own use of language. 

In conclusion, we remark that, with the more advanced 
classes in parsing and analysis, we should not restrict our- 
selves to the mere technicalities of grammar, but should 
extend the exercise so as to cover the whole subject of lan- 
guage. We may call attention to the meaning of words, to 
the peculiarities of their use, to the etymology of prominent 
terms, to idiomatic constructions, to the allusions of history 
and mythology, to the use of capitals, punctuation marks, etc.- 
We should combine the elements of rhetorical parsing with 
grammatical parsing, and so conduct the exercise as to give 
the pupil a knowledge of the correct use of language in its 
widest sense, and cultivate a critical and appreciative literary 
taste. In this way an exercise in parsing and analysis may 
be made one of the most interesting and valuable exercises in 
the entire course of study. 



CHAPTER IX. 

TEACHING COMPOSITION". 

COMPOSITION is the art of expressing our ideas and 
thoughts in words. It is the art of telling what we know, 
or of embodying our knowledge in language. This knowledge 
may consist of facts which we have observed, heard, or read; 
or of thoughts which we may have acquired by conversation 
and reading, or developed by thinking. 

Importance. — Composition is one of the most important 
branches taught in our schools. It does more to prepare a 
pupil for success in man}'- departments of life than almost any 
other branch. It also affords valuable culture to the- mind, 
for it requires closeness of observation, fullness and readiness 
of memory, and the power of original thought and generaliza- 
tion. It is valuable for its own sake; the art of correct and 
elegant expression is an accomplishment to be highly prized. 
It also cultivates a literary taste that enables one to appreci- 
ate the works of literature, and thus becomes a source of the 
most refined and exquisite pleasure. 

Composition is also, when properly taught, one of the most 
interesting and delightful of the common school branches. 
The popular dread of composition writing is due to the fact 
that it has been so poorly taught in our schools. There can 
be no intrinsic repulsiveness in writing compositions. Chil- 
dren love to talk, thej'- delight in expressing their ideas and 
feelings; and if they are taught to understand that composi- 
tion is merely writing what they know and think, as they 
would talk it, pupils would take delight in writing composi- 
tions, and long for "composition day" more than they now 

dread it. 

(286) 



TEACHING COMPOSITION, 287 

Errors in Teachinff. — The errors in teaching composition 
are numerous. Our methods give pupils a wrong idea of the 
nature of composition writing. Many pupils seem to have the 
idea that writing a composition is trying to. express what they 
do not know, or the stringing of words together after some 
mechanical model, instead of merely writing simply and natu- 
rally what they know or think about something. Pupils have 
been required to write compositions without any instruction 
or preparation for the exercise, and allowed to write blindly 
without any assistance. The subjects assigned are often un- 
suited to pupils, being too abstract and difficult. Teachers 
have made the subject too formal, and thus taken all the life, 
freshness, and zest out of it. 

Such teaching has given the pupils of bur public schools a 
dread of composition-writing. They regard it as the " bug- 
bear " of the school-room ; and think of " composition day " 
with a shudder. They perform the allotted task without any 
interest, merely because they are compelled to do so. They 
put it off to the last moment, and slip out of it whenever they 
can. They copy their compositions out of books, or get some 
older pupils to write for them. They acquire stilted and arti- 
ficial forms of expressing themselves, instead of writing in 
that natural and interesting style in which they converse. 

There is great need of reform m this respect, and this need 
seems to be widely felt. It is an oft-repeated question. How 
shall we improve our methods of teaching composition ? Our 
educational periodicals are crowded with criticisms of the old 
methods and suggestions for improvement. Authors are 
turning their attention to the subject, and text-books are 
multiplying upon it. Our grammars are growing more prac- 
tical, and text-books on Language Lessons, designed to teach 
expression, are becoming abundant. 

I>lvision of the Subject. — In the discussion of the subject, 
we shall speak first of the Preparation for Composition Writ- 
ing, and secondly, of the Methods of Teaching Composition. 



288 METHODS OF TEACHING, 

The Preparation for Coniposition will include a statement of 
those conditions and that culture which prepare a pupil for 
writing. Instruction in Composition will embrace first that 
primary instruction which is designed to prepare a young 
pupil to express himself in writing with correctness and free- 
dom. These exercises are now popularly known as Language- 
Lessons. Under the second head we shall present some 
formal directions for Writing a Comjoosition. 

I. Preparation for Composition Writing. 

Conditions. — The fundamental conditions of composition 
are, — first, something to say, and secondly, how to say it. In 
other words, composition-writing includes the matter and the 
expression. The matter consists, in a general way, of ideas 
and thoughts. For the expression of these, we need a large 
and choice vocabulary of words, and a finished and accurate 
style of expression. 

The first requirement in writing composition is, that there 
shall be something to say ; when there is nothing in the mind, 
nothing can come out of it. Here is the mistake of many 
teachers, who expect children to express ideas on a subject 
when they have no ideas to express. Ideas, thoughts, knowl- 
edge in the mind, it should be remembered, are the necessary 
antecedents to expression. In the second place, there must 
be something with which to express what we know. Our 
knowledge must flow out in the form of words; and we must 
be familiar with individual words and know how to use them. 
The third condition is that we shall acquire a clear and cor- 
rect method of expressing our thoughts ; and cultivate, so far 
as possible, those graces of style which give beauty and finish 
to expression. Let us inquire how each one of these condi- 
tions is to be attained. 

Sources of Material. — The materials of composition, as 
already stated, are ideas, facts, thoughts; sentiments, etc. 
There are several sources of these materials. The principal 



TEACHING COMPOSITION. 289 

sources of our ideas and thoughts are Observation, Reading, 
Judgment, Imagination, and Reflection. 

Observation. — Many of our ideas come from the observa- 
tion of the objects of the material world. The facts which we 
express are drawn largely from our experience of things and 
persons. Nearly all the great writers have been close ob- 
servers of nature and human nature. Homer was in deep 
sympathy with the material world, and drew some of his finest 
figures from his observation. Shakespeare was a devoted 
lover of nature, and gives us hundreds of pictures like " The 
morn in russet mantle clad, walks o'er the dew of yon high 
eastern hill," showing how close and accurate was his obser- 
vation. Dickens drew many of his characters from actual 
persons whom he knew, and whose peculiarities he had care- 
fully studied. 

Pupils should, therefore, be taught to observe closely and 
accurately. Objects should be presented to them to examine 
and describe. They should be required not only to observe 
the principal features, but also to notice the minutiae of things. 
Observation should be analytic, descending to the minor and 
less obtrusive parts of objects. Trained in this waj', a pupil 
will acquire accurate ideas of things, and be able to point 
them out and to describe what he has seen with ease and 
accuracy. 

Reading. — We can also obtain ideas and thoughts by Read- 
ing. In books we find facts, ideas, sentiments, opinions, 
figures of rhetoric, etc., which remain in our memory and may 
be used in their original form, or become types for creations 
of our own. In books are embalmed the choicest productions 
of the master minds ; and they enrich the mind of the reader, 
and give wisdom to his thought, and grace to his utterances. 
Young persons should cull in their reading the finest pas- 
sages, and write them down and commit them. They should 
also take note of the interesting and important facts in their 
bearing on the subject, and fix them in the menior}'. An 



290 METHODS OF TEACHING. 

efTort should be made to become familiar ■with the opinions 
and noble sentiments of the great thinkers, for in this way 
thought will be enriched and expression beautified. 

Judgment. — Pupils should be taught to exercise the Judg- 
ment as well as the eyes and ears; They should be taught to 
compare things, to see their relations, and to draw inferences 
fi-om them. They should be required not only to see, but to 
think about what the}'^ see ; and to form opinions concerning 
it. It is this observing with the judgment that makes the 
philosopher. By it Copernicus attained to the true idea of 
the planetary system, and Newton reached the great law of 
universal gravitation. 

Imogination. — Pupils should be taught also to exercise the 
Imagination. Everj^ form of nature not only embodies an idea, 
but may be perceived as the S3-mbol of an idea. The things 
of the material world are typical of the things of the spiritual 
world ; they are often tlie symbols of ideas and sentiments and 
feelings. Here is the source of personifications, similes, met- 
aphors, etc. The flower looks up into our eyes, the' streamlet 
bathes the brows of the drooping violets, the stars are the 
forget-me-nots of the angels, etc. It is the office of the Imag- 
ination to catch these analogies, to transmute the material 
thing into the immaterial thought, and "give to airy nothing a 
local habitation and a name." 

The Imagination ma}'^ thus be taught to leap from the visi- 
ble form to the invisible image. Things may become the 
ladder b}^ Avhich it rises to the sphere of beautiful and poetic 
thoughts. Thus, Shakespeare gives us the figure " How sweet 
the moonlight sleeps upon this bank;" Alexander Smith saj-s, 
" The princely morning walks o'er diamond dews ;" and Long- 
fellow gives us the picture of a ''silver brook" which "bab- 
bling low amid the tangled woods, slips down through moss- 
grown stones with endless laughter." The attention of the 
learner should be called to these and similar creations, and he 
should lie encouraued to create images of his own. 



TEACHING COMPOSITION". 291 

Reflection. — Much of the material of compositions comes 
from Tliiuking. We must tlierefore leani to thiuk in order 
to learn to write. It is not enough to acquire the thoughts of 
others ; we must learn to evolve thoughts for ourselves. We 
must cultivate a reflective and creative cast of mind that seeks 
for the idea lying back of the fact, that searches for the cause 
of the phenomena, and is ever inquiring what these facts prove, 
or what principle thej^ illustrate or establish. We should en- 
deavor to originate new forms of expression, new figures of 
rhetoric, and to form ideas and opinions of our own on many 
subjects. 

Sources of Words. — The second condition of becoming a 
good writer is the acquisition of words. In order to write, we 
must not only have ideas and thoughts, but we must have lan- 
guage in which to express them. The thought is to be incar- 
nated in speech. Ideas and thoughts existing in the mind, 
intangible and invisible, are to be transmuted into audible or 
visible forms. Nature, as it were, goes into the mind through 
the senses, and reappears in the form of language. Form and 
color and tone in the natural world, give form and color and 
tone to expression. The freshness of spring, the brightness 
of summer, the rich tints of autumn, and the silver habit of 
winter, all give freshness and beauty and glory to the litera- 
ture and language of a people. These words may be acquired 
in several ways. 

Indiact. — Words are derived partly by an instinctive habit. 
We pick them up ■ in conversation without any conscious 
effort. A child will often be heard to use words which it but 
a short time before heard some one else make use of. Chil- 
dren seem to have an instinct for language, and new words 
cling to their memory like burrs to the garments. A child of 
four 3^ears of age may be able to speak three or four different 
languages if it has had an opportunity to hear them spoken. 
It is, therefore, of great advantage to a child to hear a large 
and expressive vocabulary used in the household. 



292 METHODS OF TEACHING. 

Conscious Effort. — Words should also be consciously 
acquired. There should be a special effort made to enrich the 
vocabulary. We should notice the words in our reading, and 
make a list of new words, or of those which we may think do 
not belong to our practical vocabulary. Such a list may often 
be reviewed until the mind becomes familiar with it. We 
should also make use of these words in our conversation and in 
writing. It is surprising how rapidly we would improve in 
expression by the adoption of this method. Our vocabulary, 
which is often small, smaller than we think, will become en- 
larged; and we will learn to speak and write with a copious, 
rich, and elegant expression. 

The Dictionary. — The pupil should form the habit of study- 
ing the Dictionary. The dictionary has sometimes been used 
as a text-book in schools, but this is not recommended ; it 
should, however, be a student's constant companion. It should, 
lie on every student's table, and be frequently consulted. 
This has been the habit of some of the most accomplished 
scholars and writers. Charles Sumner was a most assiduous 
student of the dictionary. He had several copies in his library 
in constant use, and usuall}- carried a pocket edition with him; 
and they were found, after his death, to be the most thumbed 
of any of his books. Lord Chatham went twice through the 
largest English dictionary, studying the meaning of each 
word and its various uses. 

General Beading. — An extensive course of general reading 
is valuable in acquiring a large and choice vocabulary of 
words. Such reading should be largel}^ confined to our best 
authors, those who use words with correctness and artistic 
skill. The finished and thoughtful writer often puts a mean- 
ing in a word which we never noticed before, and thus stamps 
it upon our nlemor3^ It is onl}'^ in this wa}^ that we can ac- 
quire that nice and delicate sense in the use of words which 
distinguishes the refined and scholarly writer. 

Ancient Languages. — The study of the ancient languages 



TEACHING COMPOSITION. 293 

is especiall}' valuable in this respect. It was formerly thought 
that a knowledge of Latin and Greek was necessary in order 
to understand the English language; but this claim is now 
Seldom made. The great value of their study consists in the 
constant use of English words in the translations, and in the 
comparison and weighing of the sense of the various words' 
given in the definitions to see which will express the meaning 
of the text the most accuratel}^ If the student should forget 
every word of Latin and Greek the year after he leaves college, 
the linguistic culture he has received is a permanent posses- 
sion, and will enrich his expression. 

Small Words. — In the choice of words, young pupils should 
be careful not to select merely the large words. The large 
words attract the attention and are the most liable to be re- 
membered. It is the little words, however, that are the most 
expressive, aud are the most artistic in use. The good old 
Anglo-Saxon basis of our speech contains a richer and more 
expressive meaning than the larger Latin and Greek deriva- 
tives. Our best writers delight in the skillful use of the small 
words ; and this is an especial characteristic of Shakespeare 
and our English Bible. 

This caution is the more necessary, as young persons have 
an idea that large words indicate learning and profund- 
ity of thought. Goethe refers to this when he makes Mephis- 
topheles say to Faust, " For that which will not go into the 
head, a pompous word will stand you in its stead." This is 
quite a general opinion among the uncultured. The man who 
came to his minister, frightened at a strange appearance of 
the sun, was entirely satisfied when he was told that it was 
"only a phantasmagoria." Hazlitt, referring to the use of 
large words, says, "I hate anything that occupies more space 
than it is worth; I hate to see a load of empty bandboxes go 
down the street, and I hate to see a parcel of big words with- 
out anything in them." Leigh Hunt gave a fitting reply to a 
lady who asked the question, "Will you venture on an 



294 METHODS OF TEACHING. 

orange?" by his answer, "No, thank you, I fear I should fall 
otf." Let the pupil, therefore, not select the large words, 
but learn to use the little words, the language of the heart and 
home, with skill and artistic eifect. 

Style of Expression. — We not only need ideas and 
thoughts, and a rich vocabulary in which to express them, but 
we need also to know how to put these words together to 
produce the best results. We need to acquire a good style 
of expression. We need to acquire that ease and elegance 
of expression and that artistic skill in the use of language, 
which distinguishes the cultivated writer. In order to aid 
the pupil in this, several suggestions are made. 

Bead Extensively. — First, we remark that pupils should 
read extensively. Reading not only gives words, but it gives 
facility in the use of words and the expression of ideas. 
Pupils who have read most are usually the best writers. We 
often find in school those who are deficient in the more diffi- 
cult studies, yet who Avrite excellent compositions ; and upon 
inquiry, learn that they have read a great deal, perhaps merely 
novels. The best scholars in the school branches are often 
very poor writers, because they have done but little reading. 
By reading, we become familiar with the style of an author, 
and form a style of our own. Many distinguished men have 
formed their style by reading a few books very thoroughly. 
Lincoln received his language culture ver}' largely from read- 
ing the Pilgrim^s Progress. Kossuth's masterly knowledge 
of English was acquired by the study of Shakespeare and the 
English Bible. The unique and expressive language of un- 
cultured men, derived almost entirely from reading the Bible, 
has often been a surprise to us and demonstrated the utility 
of reading in acquiring a style of expression. 

Copy Productions. — Pupils should be required to co]>j/ lifc- 
rary productions. Copjnng an author will make a deeper 
impression than even a careful reading of one. Sight strikes 
deeper than sound ; to execute form stamps it upon the 



I 



TEACHING COMPOSITION. 295 

memory like a die. To go over a production, word by word' 
and sentence by sentence, writing it out, will impress the 
style of the author deeply upon the literary sense. I would 
therefore require pupils to "copy compositions." If a para- 
graph could be written every day on the slate or on paper, it 
would greatly aid the literary growth of the pupil. Many 
eminent writers have practiced copying the productions of the 
masters of literature. Demosthenes copied the history of 
Thucydides eight times, in order to acquire his clear, concise, 
and elegant style. 

Commit Extensively. — Pupils should be required to commit 
extensively , botii prose and poetry. Committing will make a 
deeper impression than either reading or copying. It will 
tend to fix the words and deepen the channels of thought and 
expression. It will, as it were, give one literary moulds in 
which to run his own thoughts, or dig out literary channels in 
which our thoughts and sentiments may flow. This has been 
the practice of all who have obtained excellence in the use of 
language. Burke and Pitt cultivated their wonderful powers 
of oratory by committing the orations of Demosthenes. Fox 
committed the book of Job, and drew from it his grandeur 
and force of expression. Lord Chatham read and re-read the 
sermons of Dr. Barrow until he knew many of them bj'^ heart. 

Declamation. — The old practice of " declaiming pieces" was 
of very great value to students in the culture of literary 
power. It gave them models of style and stimulated expres- 
sion. Indeed, it often did more to give a command of English 
than the whole college course. We have noticed the style of 
young men after their graduation at college, and could, in 
several instances, trace it back to the culture derived from 
their declamation pieces. 

All this preparation for writing requires time and patience. 
It cannot be acquired in a few months or a year, but is a 
matter of gradual development. Literary skill is the result 
of literary growth. A student can master a text-book in 



2/)6 METHODS OF TE-ACHING. 

geometry or algebra in a few months; but literarj'^ culture is 
the work of a life-time. It is an organic product, like the 
development of a tree. The exercises should be continued 
daj^ by day, and the result will crown the work. We shall 
now proceed to the second division of the subject, — The 
Methods of Teaching Composition. We shall divide the sub- 
ject into two parts ; Language Lessons and Composition 
Writing. 

II. Language Lessons. 

The preparatory exercises required for young pupils in 
learning to undei'stand and use the English language with 
skill, have, by common consent, received the name of Lan- 
guage Lessons. By Language Lessons we mean such element- 
ary training in the use of language as shall enable a pupil to 
understand and appreciate language, and to use it with cor- 
rectness, ease, and elegance. 

Nature and Importance. — Of the importance of such les- 
sons there can be no doubt. The primary object of education 
in language is to learm to use language. In order to learn the 
correct use of language, we must notice and use language. 
The use of language is an art ; and we learn the art' by imita- 
tion and practice. In order to learn to talk well, we must 
hear good talking and practice talking. In ord^r to learu 
to write well, we must notice good composition and practice 
w^riting ourselves. 

A system of Language Lessons conforms to nature's 
method of teaching language. The little child, prattling in 
its mother's arms, is engaged in its first lessons in composi- 
tion. The simple name, the quality and action word, the 
short sentence, etc., all come in the natural growth of the 
power of expression. In teaching, we must observe nature's 
method and follow her golden rules. A correct system of 
language lessons is founded upon the way in which a little 
child naturally learns oral and written language. 



I 



TEACHING COMPOSITIOX. 297 

A system of language lessons will also teach a child to 
acquire and produce knowledge as well as to express it. It 
cultivates the habit of observation and comparison ; and thus 
leads a child to think as well as to express thought. Subjects 
should be assigned that require attentive examination, that 
call the judgment into activity, and that lead the pupil to 
investigate and discover facts, and thus gain knowledge for 
himself. The pupil will also be taught to classify the knowl- 
edge obtained from reading, to sift its true meaning, and to 
express in his own words the thoughts of the writer he has 
studied. 

The fundamental principle of these lessons is that pupils 
are to be taught the practical use of language by the use 
of language rather than by a study of the pr-inciples of lan- 
guage. There should be an imitation of models, and a free 
and spontaneous expression of ideas, without any thought of 
the grammatical rules or principles involved. For example, 
the pupil should express himself in sentences without any 
thought of the subject and predicate of a sentence, and use 
the different parts of speech without any knowledge of them 
as parts of speech. He should use nouns and verbs without 
knowing that they are nouns and verbs ; form plurals without 
any rules for numbers ; use cases, modes, tenses, etc., without 
knowing tli»t there are such things as cases, modes, tenses, etc. 

The system of language lessons aims to teacli the use of 
language by imitation and practice rather than by the study 
of rules and definitions. The object is to give children a 
knowledge of the uses of words and the power to express their 
ideas, without clogging their memories ' with grammatical 
terms which are to them often only abstract sounds without 
any content of meaning. The pupils are brought into contact 
with living language, and not the dead dry skeleton of gram- 
matical definitions and rules ; and this living spirit becomes 
engrafted on their own language until it becomes a part of 
their nature. 
13* 



298 METHODS OF TEACMING. 

According to this principle, a knowledge of language should 
precede a knowledge of grammar. This is the historical order 
of development. The ancients knew language and could use 
it in literature, but they had very little knowledge of 
grammar. Homer sang in immortal verse, and probably 
hardl}^ knew a noun from a verb. The Iliad embodied the 
rules of grammar, without the author being conscious of 
them ; the rules of grammar were derived from the stud}- of 
the Iliad. This is also the natural oi'der, — practice precedes 
theory, the art comes before the science, — and should be fol- 
lowed in the early lessons on language. 

Another principle is that language lessons should lead to 
and be the basis of grammatical instruction. Most of our 
text-books on language lessons invert this order by basing the 
lessons in language on grammar. This is a very great 
mistake, and vitiates the whole course of instruction. The 
language lessons should prepare for and lead up to grammar. 
Grammar may then return the favor and aid in the correct use 
of language. Thus art gives birth to science, and science 
reciprocates the faror and gives perfection to art. The study 
of grammar, therefore, should not be begun until such a 
course in language lessons, as is suggested, has been completed. 

Such lessons should be begun as soon as the child can write. 
Before this it should be required to commit and •fecite little 
poems and pieces of prose. If it can hear good models of 
conversation, it will be of very great advantage in the culture 
of correct expression. 

Course of Lessons. — We shall now present an outline for a 
course of Language Lessons suitable for beginners. This is 
a mere outline and is to be filled out by the teacher in actual 
instruction. 

L Require pupils to write the navies of objects. Write the 
names of ten objects ; the names of olyects in the school- 
room; objects in the house ; ol»jects the}^ can see b}'^ looking 
out of the window; objects thej' saw in coming to school, etc. 



TEACHING COMPOSITIOX. 299 

ft 

2. Require pupils to write the names of actions. Write 
the actions of a child ; of a bird ; of a dog ; of a cat ; of a fish ; 
of a horse ; of a cow; of a cloud; of a river, etc. 

3. Require pupils to write the names of objects with the 
names of actions, forming a sentence. Give the name of the 
object, requiring them to give the name of the action ; also 
give them the name of the action, requiring them to give the 
name of the object. 

4. Lead pupils to an idea of a sentence, as asserting some- 
thing of something. Lead them to see what is a telling or 
declarative sentence, an asking or interrogative sentence, and 
a comvianding or imperative sentence. 

5. Teach them that each sentence begins with a cajntal let- 
ter ; that a declarative or imperative sentence ends with a 
2)eriod, and an interrogative sentence with an interrogation 
point. Drill them in writing sentences and correcting sen- 
tences which violate these rules. 

6. Have them write sentences introducing adjectives, ad- 
verbs, pronouns, interjections, etc. The teacher will give the 
word, and have them form the sentences. Of course the 
pupils are not to know an3'thing about these words as parts 
of speech . 

7. Show the difference between particular and common 
names, and teach the use of capitals for particular names. 
Teach also the use of cajjitals for I and 0. Have them write 
exercises involving these things, and correct sentences which 
violate their correct use. 

8. Give two words, and have pupils write sentences contain- 
ing them both; give also three words to be put in a sentence, 
four words, etc. The pupils may also be allowed to select 
the words which they are to unite in a sentence. 

9. Give" pupils sentences, with words omitted, and require 
them to insert the correct words. Such sentences can be dic- 
tated to them, the missing word being indicated by the word 
"blank." If they are written upon the board for them, the 



300 METHODS OF TEACHING. 

missing words ma}^ be indicated by a dash; as, " I saw a • 

building a in a tree." The teacher should select and 

prepare a large list of such sentences for the use of his 
pupils. 

10. Have the pupils look at an object and describe it. Have 
them describe a school-mate, a horse, a cow, a cat, a pig, the 
school-house, a barn, a church, etc. A very interesting exer- 
cise can be had in describing one another, and other persons 
whom they know. 

11. Have pupils Zoo^ at a jjictui'e, and tell you all they see 
in it, and then write it out on their slates or on paper. Pic- 
tures can be found in the primary readers, or the teacher may 
bring a large picture to school for the pupils to look at, or 
pupils may bring some pictures from home. 

12. Show them how to arrange lines of poetry^ and that 
each line begins with a capital letter. Dictate poetry to them, 
and have them copy it, getting the lines and the capitals right. 
Write some stanzas on the board, and have them criticise and 
correct them; as, 

Mary had A little Lamb. 

its Fleece was wight As snow ! 
and Every Where that marry Went ? 
The Lamb ; was shiire To go : 

13. Have pupils talk about something, and then write down 
what they have said about it. Let them learn to write their 
talk. Take such subjects as a knife, a chair, a boat, a, pin, a 
needle, a cat, etc. Parts of the body, as the eyes, the nose, 
the, mouth, the tongue, the hands, the feet, etc., are easy and 
interesting subjects for children to talk and write about. 

14. Call out a child's knowledge of an object by asking 
questions about it, and then have him write down what has 
been said, in distinct sentences. Children often know more 
about an object than they can think of. Questions will also 
lead them to discover new things about the object that they 
had not noticed before, and teach them how to look at things 
and sain a knowledge of them. 



TEACHING COMPOSITIOiSr. 301 

15. Talk to the children about something, have them repeat 
lohat you have said in their own words, and then write it out 
on their slates, or on paper. They will thus see that loritincj 
a composition is merely telling in writing what they know and 
can tell in talk. 

16. Teach them the use of the hyphen^ as connecting com- 
pound words ; and also its use at the end of a line, in con- 
necting one syllable with the sjdlable beginning the next line. 

11. Teach the use of the comma ^ as placed after the name 
addressed; as, "John, come here;" and also as connecting 
three words of a series ; as, " He saw a boy, a gii'l, and a dog." 

18. Teach the use of the period after abbreviations ; and 
make pupils familiar with the common abbreviations; as, Mr., 
Dr., Rev., Hon., Esq. Drill them on LL.D., so that they will 
not make the common mistake, "L. L. D." 

19. Teach the use of quotation marks. Show that the in- 
formal quotation is set off by the comma; as, Mary said, 
"John, come here." Show also that a divided quotation has 
two commas; as, "To be good," says some one, "is to be 
happy." 

20. Teach also the use of the colon before a quotation in- 
troduced foi'mally by such expressions as "the following," 
"as follows;" as, He spoke as follows: "Mr. President, the 
gentleman is mistaken in his facts," etc. 

21. Teach the use of the apost?-ophe in denoting possession ; 
as, John's book. Also, its use in denoting omission of letters; 
as, Ne'er, 'T is, I 've, etc. 

22. Teach the use of the exclamation pioint after interjec- 
tions; as, Oh! Alas! Pshaw! Hurrah! etc. 

23. Let the teacher read a narrative and 'ask questions on 
it, and then have the pupils reproduce it orally and in 
writing. 

24. Write sentences on the board, and have the pupils imi- 
tate them in other sentences. Write also faulty sentences for 
them to correct. Include errors upon all the things that have 
been presented in these Language Lessons. 



302 METHODS OF TEACHING. 

25. Give related simple sentences, and require pupils to unite 
them into compound sentences. Tlius, "John stood up;" 
"John spoke to his father," changed into "John stood up and 
spoke to his father." Let them also decompose compound 
sentences into simple ones; as "John and Mary went home," 
changed into "John went home," and "Mary- went home." 

26. Give them some little j^roverb, and have them write out 
an explanation of it; as, "Little children should be seen and 
not heard;" or, "Birds of a feather flock together;" or, "A 
rolling stone gathers no moss." 

2t. Require them to express sentences in different ways; 
as, " The flowers bloom very sweetly in the spring of the 
year," changed to " In the spring of the year, the flowers 
bloom very sweetly." 

28. Require them to change poetry^ into py^ose. Write a 
stanza on the board, and have them express the same thing in 
prose; as, 

"The clay is done, and the darkness 
Falls from the wings of Night, 
As a feather is wafted downward 
From an eagle in his flight," 

Changed to "When the day is done, the darkness falls 
around us as gently as a feather which falls from the wing of 
an eagle flying above us." 

29. Exercise them on misused, words and incorrect con- 
structions; as, "I expect you had a good time;" " Let Mary 
and I go out;" etc. Make a full list of the incorrect expres- 
sions in common use, and drill the pupils in their correction. 

30. Present the elements of Letter Writing. Teach the cor- 
rect form of the Date, Address, Introduction, Close, Super- 
scription, their punctuation, and the correct use of the capitals 
which occur in them. The teacher who does not understand 
the subject will find it explained in Westlake's How to Write 
Letters. 

3L Require pupils to write letters of different kinds; as 



TEACHING COMPOSITION. 303 

Business Letters, Notes of Invitation, Notes of Acceptance, 
Excuses for Absence from School, Receipts for Money, Due 
Bills, Notes, etc. 

32. Have them write a letter to a teacher, to a friend, to 
their father, to their mother, to a school-mate, etc. They will 
be interested in' writing a letter to a dog, or a horse, -or a 
bird, etc., imagining that the an,imals can understand them. 
Give them forms of letters as models for them to imitate. 

33. Teach them a few of the simple figures of rhetoric^ as 
the Simile, the Metaphor, Personification, etc. ; and require 
them to point them out in sentences and to form sentences 
containing such figures. Have them change metaphors into 
similes, and similes into metaphors, etc. 

34. Have them write little newspaper paragraphs, as an 
account of a fire, of a part}', of a runaway, of a railroad acci- 
dent, etc. Bring a newspaper into school and read such items 
of news as will interest them, and have them write little items 
in imitation of those in the paper. 

35. During all this time, have them committing and reciting 
choice selections of prose and poetry. Do not allovr them to 
repeat these mechanically without understanding their mean- 
ing, but ask questions to lead to a clear idea of what is ex- 
pressed. This will cultivate a literary taste, which lies at the 
basis of all artistic -excellence in the use of language. 

36. Give them suitable subjects and require them to write 
little compositions. Let the subjects be simple, and of per- 
sonal interest to them. Indicate the method of treatment. 
Ask questions to lead them to what should be written. En- 
courage the timid and ditfident. Suggest how to state facts, 
to say bright little things, to expi-ess ideas and sentiments, etc. 
Lead them to write naturally, expressing what they think and 
feel. Correct kindly and gently, and strive to make them love 
to write compositions. 

The above presents a very complete outline for instruction 
in Language Lessons. It is, however, merely an outline, and 



304 METHODS OF TEACHING. 

needs to be filled but for actual use in the school-room. The 
teacher should take this outline and write out a list of exam- 
ples or exercises under each head, suitable for the use of his 
pupils. No text-book in the hands of the pupils is needed 
for this work, if the teacher is properly qualified himself; but 
each teacher will find it of advantage to write out a little 
text-book for his own use in giving instruction in language 
lessons. To aid the teacher in preparing these lessons, we 
recommend the following works : Hadley's Lessons on Lan- 
guage^ Lloyd's Literature for Little Folks, Brigsby's Ele- 
ments of the English Language, and Swinton's Language 
Lessons. 

In following this outline, the teacher should make the exer- 
cises very full and complete. Do not be afraid of having too 
much under each head, for we are most liable to err by not 
giving practice enough. Let the motto be Make haste slowly. 
Give variety to the lessons, and pupils may be kept for a long 
time on each exercise suggested. Keep up a constant review 
by introducing parts of the previous exercises into each sub- 
sequent exercise. 

III. The Writing of a Composition. 

We shall now speak of teaching a pupil to write a composi- 
tion. The previous exercises have been designed for begin- 
ners, and are mainly imitative in their character; older pupils 
should depend more upon themselves, and be required to con- 
struct formal compositions. We shall speak of the subject 
under three heads : first, the Principles to guide a teacher in 
the instruction ; second, the Method of Writing a Composi- 
tion; and third, some General Suggestions on the subject. 

I. Principles of Composition Writing. — In teaching pupils 
to write a composition, the following principles should be 
borne prominently in mind : 

1. Composition is to be regarded as the expression of ivhat 
a child actually knows. The importance of this principle is 



TEACHING COMPOSITION. 305 

enhanced by the fact that it has been very generally ignored 
by teachers. Many pupils go to work at their compositions 
as if they were expected to tell what they do not know. The 
exercise is not a spontaneous production of what they think, 
but a reaching out and striving after that which they have 
never thought. This will account, to a large extent, for the 
general distaste for composition writing, and the frequent de- 
ception in respect to their authorship. Teachers, in assigning 
subjects, seem to have been oblivious of this principle, often 
giving subjects that are entirely beyond the reach of the 
pupil's experience and range of thought. 

2. Pupils should begin ivith oral compositioiis. They should 
be required to talk about objects before writing about them. 
We should begin by having pupils talk compositions before 
they ivrite compositions. Subjects can be assigned the same 
as for a written composition, time being given for preparation 
or not, as the teacher may prefer. Many of our eminent 
editors and literary men talk their literary productions, and 
have them copied by an amanuensis. 

3. Pupils should be led to see that writing a composition is 
ivriting their talk. This is the key to composition writing 
with young pupils. This principle clearly understood, would 
be like a revelation to many a pupil ; it would open up the 
way and remove the difficulties that so often seem to rise up 
mountain high before them. Many persons who talk well 
seem to grow dumb when they take a pen in hand ; what they 
need to learn is to write their talk. 

4. Do not be too critical at first. Severe criticism tends to 
discourage the pupil, and create a distaste for the subject. 
There is no exercise in which criticism wounds so deeply or 
discourages so soon as that of composition writing. Pupils 
need encouragement as well as direction. We should com- 
mend that which is worthy of praise; and, in a kindly manner, 
point out the mistakes and suggest where improvements can 
be made. 



306 METHODS OF TEACHING. 

5. Make the subject interesting. Cultivate a love for the 
expression of thought. Be an inspiration to pupils by writing 
for them and with them. Start a little newspaper in the 
school, and have them contribute to its columns. Make them 
feel that composition writing is a delightful task ; the most 
delightful exercise in the school. They will thus long for 
"composition day," instead of regarding it with dread or in- 
difference. Remembering these principles, the teacher's way 
in teaching composition will be much smoother than it has 
been, and the results will be much more satisfactory. Indeed, 
the teacher who catches the spirit of these princii)les, and ap- 
plies them proi)erly, can make the pathway all bright and 
fragrant witli l)lossoms of intei'est, both for himself and for 
his pupils. Some of the author's pleasantest recollections of 
school life are associated with his classes in composition. 

II. Writing a Composition In the writing of a composi- 
tion, there are four things which call for special attention: 
1. The Subject; 2. The Matter; 3. The Analysis; 4. The 
Amplification. 

Each of these is modified by the kind of composition to be 
written. The pi'incipal kinds of composition are as follows: 
1. Description; 2. Narratives; 3. Essays; 4. Discourses; 
5. Fictions; 6. Poems. The first and second of these consist 
mainly of a description of facts. The Essay is a presentation 
of thought or opinion ui)on some subject: in a large sense it 
may include Editorials, Reviews, and Treatises. Discourses 
are productions designed to be read or delivered: they in- 
clude Lectures, Sermons, Addresses, and Orations. Dis- 
courses usually contain both thought and description. 

Tlte Subject. — The Subject of a composition is one of the 
most important parts of the production. To select or invent 
a good subject often requires more thought and talent than to 
write the com2:)osition. The merit of a literary production 
often depends very largely on the selection of a happy and 
suggestive topic. 



TEACIIIXG COMPOSITION. 307 

It is usually best fur the teacher to assign the subject to 
the pupil. He can better adapt it to the taste and capacity of 
the pupil than the pupil can himself. Besides, the pupil may 
not only select an inappropriate subject, but will often spend 
more time in making the selection than in writing upon it. 
It also secures more variety in subjects for the teacher to 
select them, and thus gives a wider culture in writing. It 
also removes, to a great extent, the temptation to plagiarize, 
as the pupils cannot so readily find access to an article on a 
given topic as when they clioose the topic. At times, how- 
ever, pupils should be required to select and invent topics for 
themselves, as it is an excellent exercise for their ingenuity, 
and tends to cultivate independence and self-reliance "of 
thought. Pupils who have always depended on the teacher 
for subjects, become very helpless when placed in circum- 
stances where they must make their own selection. 

In assigning the subject, the teacher should be careful to 
adapt it to the pupil. Do not give abstract or lofty subjects 
about which the pupils have no ideas or knowledge. What, 
for instance, does a little child know about Contentment, or 
Immortality, or Government, or The Sublimity of Thought, 
etc.? Let the subject be one that appeals to the pupil's experi- 
ence. With young pupils, subjects like going to school, swim- 
ming, Jii^hing, skating, coasting, etc., would be api)ropriate; 
older pupils should write on subjects requiring more maturity 
of thought and experience. In all cases, let the subject be 
interesting to the writer, if possible, and one upon which he 
may express what he believes. 

Subjects should be so varied as to give practice in various 
styles of composition. Pupils should be required to write 
descriptions of objects, places, persons, natural scenery, etc.; 
they should be required to relate incidents of their observa- 
tion or experience; to write little fictions, allegories, orations, 
dialogues, etc.; and, with many pupils, an exercise in writing 
poetry will also be of real value. 



308 METHODS OF TEACHING. 

The subject must also be determined b}^ the kind of compo- 
sition to be written. If the composition is designed for a 
public audience, it should be of popular interest and suited to 
the intelligence of the audience. 

The subject should possess unity, and be clear and fresh. 
The statement of it should be simple, not too figurative, but 
happy in expression, and, if possible, striking. The manner 
of stating a subject often gives popularity to a production. A 
book frequently owes a large share of its popularity to its 
title. The title. That Husband of Iline, sold many more copies 
than the story itself merited, and became a model for the 
naming of a score of other works. 

Tlie Material. — When the subject is selected, the first 
thing is to acquire the material for the production. There 
must be something to say before we attempt to say an3'tliing. 
We cannot draw water from a dr}^ well. This getting tlie 
material is called Invention ; and it is the most difi^cult part 
of the process of composing. It is not easy to show how it 
can be done. Some hold that it is not a thing to be taught, 
that " it is a part of one's native endowment," an original 
talent and not a power to be acquired. A few suggestions 
can be made, however, which are thought to be valuable. 

The material of a composition consists of facts and thoughts. 
Facts embrace such things as have been observed b}- the 
writer or by others. The thoughts embrace opinions, senti- 
ments, figures of rhetoric, etc. This material may be obtained 
from at least five different sources; Observation, Conversation, 
Reading, Imagination, and Reflection. These are treated 
quite fully under Preparation for Composition Writing, and 
need not be discussed here. They are more or less prominent 
in supplying the material, according to the character of ;,he 
subject upon which one is writing. 

Observation — If the subject is descriptive or narrative, a 
■writer should draw first from his own observation. That 
which is stamped with a writer's personalit}^, is far more in- 



TEACHING COMPOSITION. 809 

teresting than what he gives at second hand. Some one 
happily remarks, "Do not go to Homer for a sunrise when 
you can see one every morning." In the second place, the 
writer should draw from the experience of others, which may 
be done b}^ conversation or by reading. Much can be picked 
up in conversation that will be fresh and interesting. In the 
use of books, select only those things that are most attractive, 
and endeavor to express these facts in yonr own language. 
When the material derived from these several sources is 
abundant, make use of that which seems to possess the most 
novelty. 

Try to throw the light of fancj' around this material. The 
plain fact is not of so much interest as when it is made to 
glow with the touch of imagination. Let the fact awaken an 
image in the mind, if possible; draw from it. a simile or a 
metaphor ; endue it with the life of a personification, etc. 
Many writers, like Scott and Dickens, weave the most beauti- 
ful fancies into their statements of facts and cast a charm over 
the descriptions of the most familiar objects. 

If the subject is retleetive in its character, the material will 
consist principally of thoughts and opinions. These thoughts 
and opinions are attained by thinking, by reading, and by con- 
versation. First, a writer should try to think out all he can 
for himself. The great question is, how shall he evolve or create 
thoughts by thinking? A few suggestions will be ventured. 

Rpjiection. — First, we should put ourselves in a reflective 
mood ; we should fix the mind on the subject and think about 
it. Newton said he made his great discoveries by thinking 
about them. We should surround the subject with questions. 
Asking questions is the door to all great discoveries in sci- 
ence or inventions in art. We should try to answer our 
own questions. This will give activity to our thoughts, and 
afford us something to say on the subject. Thus, if the sub- 
ject were, "The Stars," we may inquire, — What are stars? 
Whence do they come ? Why do they shine at night? Why 



310 METHODS OF TEACHING 

do they twinkle ? With what have they beeu compared ? etc. 
The answering of these questions will give a large amount 
of material for a composition on "The Stars." 

Many subjects should be developed around some leading 
thought, and we should endeavor to find this leading thought, 
which gives unity to the treatment. The leading thought of 
a discourse is the germ from which it is developed. It is 
the living principle from which it grows ; the parent idea 
which becomes the source of life to a discourse, and without 
which the words will be but a dead letter. When the germ- 
thought appears in the mind, let the understanding brood 
over it, and it will develop into a living organism of thought 
and expression. This leading thought once in the mind, will 
give rise to many other thoughts connected with it, and which 
grow out of it as the branches shoot forth from the main stem 
of a tree. If this general conception does not occur at first, 
fix the mind on the ideas that do occur, compare them and 
see what principal thought they suggest or lead to, and thus 
reach the germinal principle of the composition, going from 
the parts to the whole. 

It is proper also to think out some figures of rhetoric, some 
comparisons, similes, or metaphors to be used in the amplifi- 
cation of the material. Many such thoughts will occur to us 
in writing, and they are usually most appropriate when thus 
suggested ; but some of our best writers mark down their 
happy thoughts to be worked into their productions as they 
are needed. 

Reading. — The writer may also read books written upon or 
touching upon the subject. Some of these ideas ma}- be taken 
and used as presented, by giving credit to their author. Many 
of the thoughts can be worked up into new forms, so that they 
will be, in a certain sense, one's own property. Such an exer- 
cise will be of great value to a young writer, in teaching him 
how to think. In reading, however, one should digest and 
assimilate what he reads, so that it will appear with the stamp 



TEACHING COMPOSITION, 311 

of his own mind upon it. It will then become his own prop- 
erty and can be used at his will. 

Another suggestion in obtaining the material by reading, is 
to read authors who have written on the subject or a kindred 
one, and mark down the ideas which their thoughts suggest 
to the mind. Many authors are very suggestive of ideas. 
They seem to deal in seed-thoughts which fall into the mind 
and produce other thoughts in abundance. As we read, an 
idea seems to spring up in the mind by a sudden illumination, 
as the spark darts from the flint when struck hy the steel. 
Thus Emerson and Carlyle can be most profitably read with a 
pencil in the hand, marking down the ideas which spring up 
in the mind as the eye passes over the printed page. 

The facts of biography, history, etc., should be rallied 
around the leading ideas to support or prove the position 
taken. These facts may be culled out from the store-house 
of memory, or we may go to books and gather the material 
needed for illustration or proof. It is well for the student to 
have a " commonplace book," and mark down such incidents 
and historic statements as he thinks may be of use to him in 
writing. 

Collect Material. — This material should be written down 
on paper, as it presents itself to the mind. It is well to liaA^e 
a blank book and jot down the thoughts as they may occur 
to us, without respect to an}- particular order. This can be 
done at odd times as the thoughts present themselves, so 
that when the time comes to write composition, there will be 
a fund of material to make use of. 

The Analysis. — The material having been acquired, the 
pupil should examine it, see what is most interesting or most 
pertinent to the subject, bring together those parts that are 
similar, and make a complete outline of the method and order 
of treatment. This is called forming the plan, or the Anahj- 
sis; and is an important part of the composition. As a rule, 
it should never be omitted ; the pupil should alwa3-s ha\'e 



312 METHODS OF TEACHING. 

some general idea of the composition before he begins to write. 
In a kind of fancy writing, we may give free rein to 
thought and imagination, and allow them to play with the 
ideas that may chance to present themselves. The light and 
gossipy essays of Addison and Lamb could never have been 
written from an outline, though even in many of these there 
is a leading idea that gave shape to the production. It is an 
excellent exercise for the pupil to take different subjects and 
merely prepare outlines of their treatment. 

In forming the analysis, the composer should have in his 
mind an idea of wliat he wants to present. If the object is 
description, he should see clearly the order in which the facts 
should be stated to secure the interest of the narrative. If 
the production is reflective, he should knov/^ what he desires 
to prove or to impress, and arrange the points in such a way 
as best to secure this object. Care should be taken that there 
be no abrupt breaks between the parts, but that one part flows 
naturally out of and into another. It will be well sometimes 
to try different arrangements, and see whicli seems best. A 
writer will often change the whole plan of his essay while he 
is writing it out, as a general changes his plan of attack on 
the field of battle; but this is always inconvenient and haz- 
ardous. A very great deal of good judgment ma}^ be shown 
in the analysis of subjects, and the success of a lecture or ad- 
dress is often largely due to the arrangement of its parts. 

The A)npIi/ic((fion. — Having formed the plan of the com- 
position, the next step is the Amplification. The facts and 
thoughts are to be presented in an orderly manner; care is to 
be taken that the sentences are clear and correct, that the 
matter is properly connected, that the style is suited to the 
subject, etc. Many new ideas and illustrations will present 
themselves in the course of the amplification; and when ap- 
propriate should be wrought into the composition. 

Tliere are three parts of a literary production thnt requiro 
especial attention. These are the Tnfrodvcfion, the Body, and 



TEACHING COMPOSITION. 313 

the Close. In an ordinary short school essay, these divisions 
are not so marked ; and yet they are not to be overlooked even 
there. Every production should have a fitting opening and 
closing thought; it should neither open nor close with an 
awkward abruptness. In lengthy essays, lectures, orations, 
etc., these divisions should be distinctly marked. 

The Introduction — The Introduction should be modest, 
appropriate, lively, and interesting. It should not promise too 
much, or the expectations it raises may be disappointed. It 
should grow naturally out of the subject, and be a natural in- 
troduction to what is to follow. It should be suited to attract 
notice, and to prepare the mind to listen with attention and 
an expectation of pleasure to what follows. An interesting 
incident, an apt illustration, a humorous remark, etc., are 
often used by good writers and speakers as an introduction. 
In an oration, the introduction should have an air of candor 
and modesty ; it should be calm and moderate, and not antici- 
pate the main points of the discussion. 

Cicero laid down the rule that the Introduction should be 
written last, though he did not always follow his own precept. 
He was accustomed to prepare introductions and lay them 
aside to be used when needed. On one occasion, he inadver- 
tently used the same introduction twice ; and upon being in- 
formed of it by Atticus, he confessed liis error, and prepared 
a new one. 

The Body. — In the Bod}' of the essay, the subject should be 
formally developed. The leading idea should be kept care- 
fully in mind, and the effort be made to unfold it. There 
should be an organized growtli of thought and expression in 
which all the subordinate ideas are gathered around the prin- 
cipal one. A thread of related thought should run unbroken 
through the entire exposition, binding all tlie parts together 
in symmetry and unity. 

In view of this, the different points to be presented should 
be ari-anged iu the best order. If there are objections to be 
14 ' 



314: METHODS OF TEACHING. 

answered, it is usually best to attend to them first. Having 
cleared the way of these, the direct arguments may then be 
presented, throwing the less plausible ones in the middle, and 
thus giving the stronger ones first and last. The exhortation 
and appeal to the feelings come appropriately toward the 
close, but an incidental appeal may be made at different times 
as the occasion offers. 

If humorous passages occur in a spoken discourse, they 
should not come in too near the beginning, or they will unfit 
the minds of the hearers to listen to what follows. So also it 
is not well to touch the feelings with pathos near the early 
part of the discourse, for it will be difficult to hold the inter- 
est after the reaction of feeling takes place. It is well also 
that the production should increase in majesty and grandeur 
of expression towards its close. 

Care should be taken that the thoughts bo expressed in an 
attractive and pleasing form. The language should be simple, 
clear, and impressive. When suitable, it may be adorned 
with figures of rhetoric and pictures of the imagination. 
Nothing should be introduced, however, for mere ornament, 
and that does not contribute to the main purpose of the 
essay. Much self-denial is often required to avoid putting 
words or figures into a production when their only claim is 
their beauty. It is in this that the difference between a culti- 
vated and an uncultivated writer is readily noticed. 

The Conclusion. — The Conclusion, or Peroration of a dis- 
course, like the Introduction, requires especial care. The 
object is to leave as deep an impression on the mind of the 
reader or listener as possible. This is sometimes done by re- 
serving the strongest or most impressive head of the discourse 
for the last, and ending with it. Sometimes the writer or 
speaker gives a brief and striking summary of the whole dis- 
course, bringing it all, in rapid succession, again before the 
mind. In this way the conclusion becomes a kind of burning- 
glass which gathers into a focal point all the separate rays of 
the production. 



TEACHING COMPOSITION. 315 

The conclusion ma}' often consist of an exhortation or 
appeal to the feelings, in view of wliat had been stated. Ac- 
cepting the views of the writer or speaker, the reader or lis- 
tener is prepared to sympathize with his feelings and to share 
in his emotions. In eveiy case, where there is a formal con- 
clusion, it should seem to flow naturally out of the discussion 
and be appropriate to it and the subject. 

Dr. Hart says, "The main thing to be observed is to hit 
upon the precise time for bringing the discourse to a point. 
If this is done too abruptl}^, it leaves the hearers expectant 
and dissatisfied. If, when the discourse seems ended, and the 
hearers are looking for the close, the speaker continues turn- 
ing round and round the point, without coming to a pause, 
the audience becomes restless and tired. There are, indeed, 
very few speakers that know how or when to stop." 

In this discussion of composition writing, we have lifted the 
subject up into the plane of preparing a lecture or an oration; 
but it will be seen that the suggestions given nearly all apply 
to the writing of an ordinary school composition. A compo- 
sition, if tlioughtful, is a little lecture or a little oration, and 
is designed to prepare for these larger productions; and the 
same methods and principles that apply to one apply also to 
the other, the difference being one of degree only. We close 
the subject with a few general suggestions. 

III. General Suggestions. — There should be frequent ex- 
ercises in writing composition. In many schools pupils are 
required to write once in two weeks. It would be better, 
however, to have them write every week; and still better to 
have the exercise more frequentl}^ 

Paper, Writing, etc. — The pupils should be required to 
write on paper of a uniform size. The large-sized letter- 
paper, known as "Bath post," is perhaps the most convenient. 
The subject should be written at the top of the page on the 
middle of the first line ; and a blank line left between the 
heading and the composition. There should be a margin of 



816 METHODS OF TEACHING. 

about one inch on the left-hand side of each page, to allow 
room for corrections. The first line of each paragraph should 
be indented about one inch. The writing should be neat and 
legible, with no flourishing or fancy writing ; and care should 
be taken with respect to the paragraphs, etc. The signature 
should be written on the next line below the close of the com- 
position, near the right-hand edge; and the name of the place 
and date on the next line below the signature, near the left- 
hand edge. The compositions should all be folded alike, in 
three divisions; and the name of the writer, the subject, and 
the date, be written on the back. If an outline is required, 
it may be written either at the beginning or close of the 
composition. 

Corrections. — The compositions should be handed in 
promptly at the time appointed, for correction. The correc- 
tions, as a rule, should be made by tlie teacher; though at 
times the essa3^s may be distributed among the members of 
the class for correction, under the general supervision, how- 
ever, of the teacher. The corrections may include errors in 
orthography, punctuation, use of capitals, hyphens and apos- 
trophes, construction of sentences, figures of rhetoric, st3-le 
of expression, general development of the subject, etc. The 
closeness of the correction should be adapted to the age and 
ability of the pupils. Severe criticism will tend to discourage 
young pupils, who are especially sensitive in respect to their 
own compositions. 

It will be best for the teacher, as a rule, to indicate the 
errors, rather than to correct them, requiring the pupils to 
make the correction. This will make a deeper impression 
upon the mind than when the teacher makes the corrections 
for them, and will lead them to be more careful not to repeat 
the mistake. In order to indicate the errors, some system of 
notation should be used. A line may be drawn under each 
error, and the symbol indicating the nature of it be written in 
the margin. The notation used in our own school, is as fol- 



TEACHING COMPOSITION. 317 

lows: ^ for anal3'sis ; 0, orthography ; G^, grammar; TF, wrong 
word ; /S, sentence ; P, punctuation ; etc.. For a fuller statement 
of the system, see Westlake's Three Thousand Practice Words. 

The teacher may sometimes take the compositions into the 
class and call attention to the errors, withholding the name of 
the writer, if he chooses, and invite corrections and sug- 
gestions. The pupils may also be required to read the errors 
marked, and correct them orallj', or write them upon the 
board with their correction. Some teachers require pupils to 
copy the composition in a book provided for the purpose, with 
the mistakes all corrected. 

Read'uig Conijtositioiis — There should be a time set apart 
for the reading of compositions. This is a very useful exer- 
cise, and may be made the nijeans of a great deal of literary 
culture. In this exei'cise, each pupil may read his own pro- 
duction, or one may read for another, as the pupils or teacher 
may prefer. After the reading of a composition, remarks and 
criticisms may be made, first by the pupil and then by the 
teacher. Care should be taken that the attitude, expression, 
etc., of the reader be free from error. Pupils may often be 
required to commit their essays and recite or declaim ihem, 
those designed for declamation being written in the style of 
an oration. 

The exercises of "composition day" may be made very in- 
teresting and instructive by varied literary exercises. A 
paper, with an appropriate name, to which the pupils contrib- 
ute, will give variety to their productions and be of great 
interest to the pupils. It may contain short essays, editorials, 
items of news, amusing incidents, wit, humor, poetry, adver- 
tisements, etc. Some orations, recitations, dialogues, and 
debates will also give additional interest to the occasion. 
The class may occasionally be resolved into a literary societ^y 
with regular officers and a progi'amme of exercises, consisting 
of an inaugural address, orations, recitations, essays, answers 
to referred questions, a paper, etc. 



318 METHODS OF TPJACHINQ, 

111 conclusion, we remark that the teacher should spare no 
pains to ci'eate an interest in literary culture. No greater 
intellectual benefit can be conferred upon a pupil than to cul- 
tivate in him a literary taste and train him to an appreciation 
of literary productions. That teacher achieves a great success 
and accomplishes a valuable work, who makes composition 
writing a pleasing task and composition day to be regarded 
with interest and delight. 



MATHEMATICS. 



CHAPTER I. 

THE NATURE OF MATHEMATICS. 

MATHEMATICS is the science of Quantity. It seeks to 
ascertain tlie relations and truths of quantity, and to de- 
rive unknown quantities from other quantities that are 
known. This definition indicates the general nature of the 
subject, though it is not entirely free from objections. Many 
attempts have been made to frame a philosophical deflnitioa 
of mathematics, but none has yet been presented wliioh is gen- 
erally acceptable. 

The term Mathematics is derived from the Latin mathemat- 
ical or the Greek malhematike^ which comes from mallieaia, 
learning. The use of the word in the plural form indicates 
that this department of knowledge was formerly considered 
not as a single branch, but as a group of several branches, 
similar to our use of the phrase, the mathematical sciences. 
Previous to the present century, nouns ending in ics, as 
optics^ mechanics, etc., were construed with a verb in the 
plural ; but they are now generally regarded as singular. 

The fundamental branches of mathematics are Arithmetic 
and Geometry. This classification arises from the nature of the 
two kinds of quantity considered. The two general divisions 
of quantity arc Number and Extension: the science of number 
is Arithmetic; the science of extension is Geometry. These 
two branches have also been distinguished with respect to 
their relation to Time and Space. Extension has its origin 
in Space, and number in Succession, which is only i)ossible in 
Time. Hence,. Geometry has been called the science of Si)ace, 

(319) 



820 .METUOnS OF TEACHING. 

and Arithmetic the science of Time. Geometry has also been 
called the science of Form, since it treats of the possible 
forms of space. 

If we introduce general symbols for numbers, and develop 
a science with them, we have another branch of mathematics, 
called Algebra. If we use these general symbols in investi- 
gating geometrical magnitudes, we obtain another branch 
called Analytical Geometry. If we investigate quantitj'^ by 
considering the infinitesimal elements of which it is com- 
posed, we obtain a branch called Differential and Integral 
Calculus. 

There is another method of conceiving the subject of quan- 
tity and reaching a division of the science. Quantity is of 
two kinds; discrete and continuous. Discrete quantity is 
that . which exists in separate parts, forming quantity of 
multitude or number; as a number of men, trees, etc. Con- 
tinuous quantity is that, which does not exist in separate 
parts, or is that in which the parts are connected together in 
one whole, as length, time, etc. Discrete qiaantity is immedi- 
ately expressed in numbers, and gives rise to the science of 
arithmetic. Continuous quantity cannot be immediately ex- 
pressed in numbers ; a part of the quantity must be taken as a 
unit of measure in order to express it numerically. One form 
of continuous quantity, that which belongs to space, gives 
rise to the science of geometry. 

Thei'e is no general agreement among writers in respect to 
the philosophical division of the science of mathematics. 
Comte, the most celebrated writer on the philosophy of 
mathematics, divides the science into two parts; Concrete 
Mathematics and Abstract Mathematics. Under Concrete 
Mathematics he includes Geometiy and Rational Mechanics ; 
under Abstract Mathematics he includes the Calculus, which 
embraces Arithmetic, or the Calculus of Values, and Algebra, 
or the Calculus of Functions. The latter, called also Analy- 
sis, embraces ordinary algebra, in which the equations are 



THE NATURE OF MATHE1\:ATIC3. 321 

di7'ectly established between the magnitudes under considera- 
tion, and the Transcendental Analysis, in which the desired 
equations are derived by invariable analytic methods from 
_ equations between quantities indirectly connected with those 
of the problem. These are distinguished as the Calculus of 
Direct Functions and the Calculus of Indirect Functions. 

Materials. — A knowledge of mathematics consists of 
Ideas and Truths. The Ideas of mathematics represent the 
different forms of quantity which present themselves for con- 
sideration. The Truths of mathematics are the relations that 
exist between the quantities. When we conceive and examine 
the different forms of quantity, we perceive some truths that 
are self-evident ; such truths are called axioms. By means of 
these axioms we compare the different quantities, and attain to 
other truths; these truths are said to be derived by reasoning. 
The ideas and axioms are thus the basis upon which, by the 
process of reasoning, we build up the science of mathematics. 

The Ideas. — The Ideas of mathematics are not merel^^ ideas 
or products of the mind. They represent realities, things 
which have an objective existence. They are not ideas of 
material things, there is no tangible reality corresponding to 
them, but they are real forms of space and number. The 
forms of geometry are pure forms, forms not filled with con- 
tent ; and the numbers of arithmetic are pure numbers, inde- 
pendent of any association with material things. But in both 
cases the quantities are realities which admit of application 
to the objects of the material world. 

Definitions. — The description of the ideas of mathematics 
in clear and exact language gives rise to the Definitions of 
the science. The Definitions of mathematics may thus be re- 
garded as the precise description of its ideas. The ideas are 
antecedent to the definitions, and are the basis of them. In 
teaching the science, definitions are employed to lead the mind 
of the learner to clear conceptions of the ideas. On account 
of the intimate relation between the idea and the definition, 
14* 



322 METHODS OF TEACHING. 

some writers state that the foundation of mathematics is 
definitions and axioms, rather than ideas and axioms. 

Axioms. — The Axioms of mathematics are the self-evident 
truths of the science. They are intuitive truths which arise 
in the mind immediatelj^ on the contemplation of the various 
forms of quantity, without any process of reasoning. They 
express a self-evident and necessary relation between quanti- 
ties, and thus involve a comparison or a judgment. Given 
the several conceptions, and the truth is immediately^ per- 
ceived b}^ a direct comparison, without any intervening pro- 
cess of thought. 

Axioms are the basis of mathematical reasoning. Without 
some self-evident truths as a starting point, no process in 
thought is possible. By some the}' are regarded as general 
truths which contain the particular truths of the science, and 
from which the particular truths are evolved by reasoning. 
It seems more correct, however, to regard them as laws which 
direct or govern the comparisons of the reasoning process. 
Thus the truth that "things that are equal to the same thing 
are equal to one another," is a law to guide us in comparing 
quantities, rather than a general truth that contains the other 
truths of mathematics. 

Beamning. — The Reasoning of mathematics is deductive. 
It deals with necessary truth, and derives the relations by 
universal and necessary laws of inference. The basis of the 
reasoning is the definitions and axioms, or in other words, the 
conceptions and the self-evident truths arising out of these 
conceptions. Thus having a conception of a triangle and a 
right angle, we ma}^ by comparison, in accordance with the 
laws of inference, derive the truth that "the sum of the 
angles of a triangle equals two right angles." So in arith- 
metic, having a conception of some subject, as the greatest 
common divisor, we can derive a method of obtaining the 
greatest common divisor of two numbers, guiding the investi- 
gation by the self-evident truths that pertain to the subject. 



THE NATURE OF MATHEMATICS. 323 

Viilue of 3£atheinatics, — Mathematical studies have in 
all ages been A'alued for the mental discipline they atford. 
There is probably no single study pursued in the schools 
which develops the mind in so many wa^'s, and is so well 
adapted to every stage of mental growth as mathematics. 
Mathematical studies give some culture to perception and 
memory, faculties which it has been thought they almost 
entirely neglect. They require the most complete mental 
concentration, and thus aftbrd the highest culture to atten- 
tion. Dealing with the relations of quantity, they give con- 
stant exercise to the judgment, and train it to the closest 
discrimination of similarity and difierences. Every derived 
truth is a logical deduction from premises, and is reached by 
the continued operation of the power of reasoning. The first 
truths are axiomatic, and are comprehended only in an act of 
intuition, which gives exercise to the Reason. 

The Imagination is also active in geometry in picturing the 
parts of the figures upon which we reason, and in creating 
diagrams to discover new relations. All the definitions are 
"logical definitions," and as such train to the nicest percep- 
tion of the relation between ideas and their expression. In 
fact there is no one science that brings so large a number of 
the faculties of the mind into so constant and forcible an 
activity, and especially those faculties which give strength 
and dignity to the intellect, and glory to scientific achieve- 
ment. That it does not train to habits of probable reasoning, 
and does not give facts for induction and for opinions on 
social and political questions, is admitted; but that it does 
more than an}- other scliool stud}^ to give mental power and 
logical habits of thought, must be admitted. 

Eleinentary Branches. — The three elementary branches of 
mathematics are Arithmetic, Algebra, and Geometry. These 
are taught in all our graded and high schools, and should, in 
their elements at least, be taught in the ordinary con)mon 
schools. We shall in this work discuss the methods of teach- 
ing these three branches. 



I 



CHAPTER II. 

THE NATURE OF ARITHMETIC. 

THE science of arithmetic is one of the purest products of 
human thought. .It was aided in its growth by the rarest 
minds of antiquity, and enriched by the thought of the pro- 
foundest thinkers. Over it Pythagoras mused with the 
deepest enthusiasm; to it Plato gave the aid of his refined 
speculations ; and in unfolding some of its truths Aristotle 
employed his peerless genius. In its processes and principles 
shines the thought of the ancient and modern world; the 
subtle mind of the Hindoo, the classic culture of the Greek, 
and the practical spirit of the Italian and Englisliman. It 
comes to us adorned with the offerings of a thousand intel- 
lects, and sparkling with gems of thought received from the 
great minds of nearly every age. 

Like all science, which is an organic unit}^ of truths and 
principles, the science of arithmetic has its fundamental 
ideas, out of which ai'ise subordinate ones, which themselves 
give rise to others contained in them, and all so related as to 
give symmetry and proportion to the whole. These funda- 
mental and derivative ideas, the law of their evolution, and 
the philosophical thread that runs through them and binds 
the parts together into an organic unity, should be, understood 
by the teacher. 

To aid the teacher in acquiring a more philosophic concep- 
tion of arithmetic than he obtains from the text-book, we shall 
speak of the General Nature of the science, its Language, 
Reasoning, and Methods of Treatment. We shall then pro- 
ceed to consider the Methods of Teaching the subject. 

(324) 



NATURE OF ARITHMETIC. 



I. The General Nature of Arithmetic. 

Definition. — Arithmetic is the science of numbers and the 
art of computing with them. The term is derived from 
arithmetike, which is from arithmos, meaning number. This 
is the definition usually given, and is sutHciently correct for 
all practical purposes. There are some writers, however, who 
hold that Arithmetic is onlj^ one of the sciences of numbers, 
Algebra and Calculus being also regarded as sciences of num- 
l)er Some French writers call the general science of numbers 
Numerique; and divide it into Arithmetic, the science of 
special numbers; and Algebra, the science of number in gen- 
eral. Sir Isaac Newton called algebra Universal Arithmetic. 
The Nature of Nmnber. — The basis of arithmetic is 
Number. A number is usually defined as a unit or a collec- 
tion of units, a definition derived from Euclid. This definition 
is liable to the objection that & number and a collection are not 
quite identical in meaning. Many definitions of a Number 
have been attempted, but none has yet been given which is 
entirely satis factor}'- to mathematicians. The simple idea of 
a number is that it is the how-manij of a collection of objects, 
and it might be so defined. The definition first given is, 
however, the one generally preferred by writers on arithmetic. 

There are three fundamental classes of numbers ; Integers, 
Fractions, and Denominate Numbers. These three classes are 
practically and philosophically distinguished, and constitute 
the basis of a threefold division of the science. Logically the 
distinction is not entirely without exception, since a fraction 
may be denominate, and a denominate number may be inte- 
gral; but the division is regarded as philosophical, since these 
tliree classes of numbers not only differ in character, but re- 
quire distinct n:iethods of treatment, and give rise to distinct 
rules and processes. 

Integers. — An Integer is a number of integral units. These 



S2Q METHODS OF TEACHING. 

units are regarded as individual or whole, and hence an Inte- 
ger is called a whole number. There is no relation of the 
things numbered to any other thing regarded as a unit; but 
simpl}^ the relation of the collection to ,a single thing of the 
collection. An integer is thus a pure product of S3mthesis. 

Fractions. — The Unit, as the basis of arithmetic, may be 
multiplied or divided. A sj^nthesis of units, as we have seen, 
gives rise to Integers; a division of the Unit gives rise to 
Fractions. Dividing the unit into a number of equal parts, 
we see that these parts bear a definite relation to the integral 
unit, and name them from this relation. These parts may be 
regarded as individual things, and constitute a particular 
class of units called fractional units. The collection and 
numbering of these fractional units give rise to a particular 
class of numbers called Fractions. 

Denominate Numbers. — Quantity is of two kinds — quantity 
of multitude and quantity of magnitude — called also discrete 
and continuous quantity. Discrete quantity exists in indi- 
vidual units and is immediately estimated as how many; 
continuous quantity exists in the mass, and is primarily esti- 
mated as how much. Thus we say how many apples, how 
many trees, etc., while we say how much money, how much 
land, etc. Quantity of magnitude does not primarily admit of 
numerical expression ; to thus express it, we fix upon some 
definite part of the quantity as a unit of measure, and express 
the quantity by the number of times it contains the unit of 
measure. Continuous quantity thus becomes expressed as 
discrete quantity; the how much is reduced to the how many; 
and a new class of numbers arises, called Denominate Nu7n- 
bers. These units being of different sizes and bearing difl;er- 
ent relations to one another, require a special method of 
treatment which gives rise to a distinct department of arith- 
metic. With the adoption of the meti'ic system, this part of 
arithmetic will lose the distinctive character of its operations. 

Logical Outline of Arithmetic. — The science of Arithme- 



THE NATURE OF ARITHMETIC. 827 

tic is based upon and is developed from these three classes 
of numbers. Its several parts are evolved from the possible 
operations upon these numbers. A consideration of these 
possible operations will give us a Logical Outline of Arith- 
metic. 

All numerical ideas begin at the Unit. The Unit is the 
origin, the basis of arithmetic. The Unit can be multiplied 
and divided ; hence arise Integers and Fractions. Each 
Integer is a synthetic product derived from a combination of 
units ; each Fraction is an analytic product derived from the 
division of the unit. Having obtained numbers by a synthesis 
of units, we may unite two or more numbers, and thus obtain a 
larger number by means of synthesis; or we may reverse the 
operation and descend to a smaller number by means of analy- 
sis. Hence the two fundiamental operations of arithmetic are 
Synthesis and Analysis. To determine when and how to 
unite and separate numbers, we employ a process of reasoning 
called comparison. This process compai-es numbers and de- 
termines their relations ; it is the thought process of arithme- 
tic, as analysis and synthesis are the mechanical processes. 
Comparison directs the original processes of arithmetic, mod- 
ifies them so as to produce from them new^ ones, and also itself 
gives rise to other processes not contained in or growing out 
of the original ones. Comparison is thus the process by which 
the science is constructed ; it is the key with which the learner 
unlocks its rich store-house of intei'est and beauty. 

Synthesis. — A general synthesis is called Addition. A 
special case of the sj-nthetic process of addition, in which 
the numbers added are all equal, is called MultijMcation. 
The forming of Composite Numbers bj' a synthesis of factors, 
which we call Composition, Multiples formed b}^ a sjnithesis 
of particular factors, and Involution, a synthesis of equal 
factors, are all included under Multiplication. Hence the 
process of Addition includes all the synthetic processes to 
which numbers can be subjected. 



328 METHODS OF TEACHING. 

Analysis — A general analysis, the reverse of Addition, is 
called Subtraction. A special case of Subtraction, in which 
the same number is successively subtracted with the object of 
ascei-taining how many times it is contained in another, is 
called Division. A special case of Division, in which many or 
all of the makers ox factors of a number are required, is called 
Factoriiig ; a special case of Factoring, in which one of the 
several egwaZ /actors is required, is called Evolution ; find a 
case in which some cornmon factor is required, is called Com- 
mon Divisor. Hence the process of Subtraction includes all 
the analytic processes to which numbers can be subjected. 

Gompa.rison. — By comparison the general notion of relation 
is attained, out of which arise several distinct arithmetical 
processes. By comparing numbers we obtain the idea of 
Batio, arithmetical and geometrical. A comparison of equal 
ratios gives us Proportion. A comparison of numbers differ- 
ing by a common ratio gives us Arithmetical Progression and 
Geometrical Progression. In comparing numbers of different 
units, we observe we may pass from one to another of differ- 
ent species under the same genus, and thus have the process 
of Reduction. In comparing numbers, we may assume some 
number as a basis of reference, and develop their relations in 
regard to this basis ; when this basis is a hundred, we have 
the process of Percentage. In comparing numbers, we dis- 
cover certain relations and peculiarities which give rise to 
the Properties or Principles of numbers. 

Remarks. — We thus derive a complete outline of the science 
of numbers. Arithmetic is seen to consist fundamentally of 
three things ; Synthesis, Analysis, and Comparison. Synthe- 
sis and Analysis are fundamental mechanical operations; 
Comparison is the fundamental thought-process which con- 
trols these operations, brings out their potential ideas, and 
also gives rise to other divisions of the science growing out 
of itself. The whole science of pure arithmetic is the out- 
growth of this triune basis, — S^'nthesis, Analysis, and Com- 



THE NATURE OF ARITHMETIC. 329 

parison. The rest of arithmetic consists of the solution of 
problems, either real or theoretical, and may be included 
under the head of Applications of Arithmetic. 

This outline of the science grows out of the idea of pure 
number, independent of the language of arithmetic. These 
fundamental processes are modified by the method of nota- 
tion adopted to express numbers. With the Roman or Greek 
methods of notation, the methods of operation would not 
be the same as with the Arabic system. The method of 
adding by " carrying one for every ten," of subtraction by 
"borrowing," a portion of the treatment of common and deci- 
mal fractions, the methods of extracting roots, etc., are all 
largely due to the system of notation adopted, and many of 
them have their origin in the Arabic system. It may be 
remarked, also, that the power of arithmetic as a calculus 
depends upon the beautiful and ingenious s^'stem of notation 
adopted to express numbers. 

II. The Language of Arithmetic. 

The expression of the fundamental ideas of arithmetic gives 
rise to Arithmetical Language. This language is both oral 
and written. The oral language is called Numeration ; the 
written language is called Notation. Numeration is the 
method of naming numbers and of reading them when ex- 
pressed in written charactei's. Notation is the method of 
expressing numbers in written characters. 

Ntiineration. — In naming numbers we do not give each 
number an independent name, but proceed upon the principle 
of naming a few numbers and then forming groups or collec- 
tions, naming the groups, and using the first names to num- 
ber the groups. This ingenious, though simple and natural, 
method of naming numbers by forming groups or classes, 
seems to have been adopted by all nations. It has the advan- 
tage of employing but a few names to express even very 
large numbers, and of enabling the mind, by the principle of 



330 METHODS OF TEACHING. 

classification, to conceive quite i'eadil_y of a number otherwise 
entirely bej^ond its powers of conception. 

Thus, after naming the numbers as far as ten, we regard the 
collection teii as a single thing, and count 07ie and ten, two and 
ten, etc., up to twenty ; and then continuing in the same way, 
we have tivo tens and one, two tena and two, etc., up to three 
tens; and so on until we obtain ten of these groups of tens. 
These ten groups we now bind together by a thread of thought 
forming a new group which we call a hundred ; and proceed- 
ing from the hundred in the same way, we unite ten of these 
into a larger group, which we name thousand, etc. The 
names of the numbers immediately following the first group 
are not quite in the form suggested ; but they involve the 
principle named. Thus, instead of one and ten, we say 
eleven, from the Saxon endlefen, or Crothic ainlif (ain, one 
and lif, ten); and instead of two and ten, we say twelve, from 
the Saxon twelif, or Gothic tvalif (tva, two, and lif, ten). 
The names of the numbers following these have been modified 
and abridged by use, though in the present form they suggest 
the original expression and show the principle of naming 
numbers. 

Origin of Names. — The origin, or primary meaning of the 
names applied to the first ten numbers, is not known. It has 
been supposed that the names of the simple numbers were 
originall^'^ derived from some concrete objects, and probably 
from some part of the person. Many tribes have used the 
term hand to express fve, and 7nan for twenty. Humboldt 
says that the Indians of New Grenada use ata, water, for one; 
bosa, an inclosure, for two; mica, changeable, for three; etc. 
Prof. Goldstiicker giA^es the following theory for the origin of 
the Sanskrit numerals, and thus of our own, which are de- 
rived from the Sanskrit: One, he says, is "he;" two, "diver- 
sity ;" three, " that which goes beyond ;" four, " and three," 
that is, "one and three;" five, "coming after;" six, "and 
four," tluit is, "two and four;" seven, "following;" eiglit^ 



THE NATURE OF ARITHMETIC. 331 

"tvvo foiu's ;" nine^ "that which comes after ;" ten, " two and 
eight/' Thus only one and two have distinct original meanings. 

After reaching the thousand it will be noticed tliat a change 
occurs in the method of grouping. Previously, ten of the old 
groups make one of the next higher group ; but after the 
third group, or thousand, it requires a thousand of an old 
group to make one of the next group which receives a new 
name. Thus a group of a thousand thousands is called a 
million; n. thousand millions, a billion, ei^i. This change in 
th( law of naming groups is not a thing of chance, but of 
science ; as it is a matter of great convenience in naming the 
larger numbers. 

Notation. — In writing numbers, we do not use common 
words, nor have a special character for each number. The 
method of notation is based upon the principle of using a. few 
characters to express the first few numbers, and expressing 
the groups by the position of these characters. The founda- 
tion principle is that of place value, the groups being repre- 
sented by the simple device of place. 

This method seems to have originated among the Hindoos, 
and is now adopted by all civilized nations. It is usually 
called the Arabic S3^stem, from the fact that it was introduced 
into Europe through the Arabs; and was for a time supposed 
to have originated with them. The methods of notation used 
by the Greeks and the Romans were much inferior to that of 
the Hindoos, so much so that it was impossible to employ 
the Roman system, at least, in calculations. 

The invention of the Arabic system of notation is one of 
the greatest achievements of the human mind. Without it, 
many of the arts would never have been dreamed of, and the 
science of astronomy would still be in its -cradle. With it, 
man becomes armed with prophetic power, predicting eclipses 
and occultations, determining the existence of worlds which 
the eye. of the telescope had never seen, and marking out with 
unerring accuracy the orbits of planets and thejr position in 
the heavens for centuries to come. 



332 METHODS OF TEACHIXQ. 

Origin of Characters. — The origin of the characters is not 
definitefy known. Three theories have been given for them, — 
that of a combination of straight lines, that of a combination 
and modification of angles, and that of initial letters. It has 
been supposed that people began to represent numbers by 
straight lines, and that these might have been combined into 
our present Arabic digits. It has also been supposed that 
angles may have been used to indicate numbers, and that 
a combination of these might have been modified into the 
present forms. Prinseps, a profound Sanskrit scholar, thinks 
that they were originally the initial letters of the Sanskrit 
numerals. This theory is rendered plausible from the fact 
that the Romans, Greeks, and Hebrews used letters to repre- 
sent numbers. 

The origin of the cipher, by the first of these theoi'ies, is 
accounted for by supposing it to have been represented by a 
circle, suggested by counting around the fingers and thumb 
held in a circular position. By the second theory, if charac- 
ters with angles represented numbers, a character with no 
angles, like a circle, would represent nothing. The third 
theory does not account for the zero, the most important 
character of them all. " It would be highly important," says 
Max Miiller, " to find out at what time the naught first occurs 
in Indian inscriptions. That inscription would deserve to be 
preserved among the most valuable monuments of antiquity, 
for from it would date in reality the beginning of true mathe- 
matical science, — impossible without the naught, — na}', the 
beginning of all the exact sciences to which we owe the inven- 
tion of telescopes, steam engines, and electric telegraphs." 

The Numerical Base. — The basis of the method of ex- 
pressing numbers'is decimal. This arises from the fiiet that 
arithmetic had its origin in counting the fingers of the two 
hands. There are traces in several languages of otiier numbers 
besides ten being used as the basis of the system of counting ; 
but all civilized nations have counted by tens. From this 



THE NATURE OF ARITHMETIC. 333 

general use of the decimal scale, it has been inferred that it 
possesses some intrinsic excellence; yet the fact is, that it is 
liable to many objections, a few of which we will mention. 

First, the decimal scale is unnatural. A grouping b^^ tens 
is seldom seen in nature or art. Nature groups in jjair^, in 
threes, \i\ fours/\n fives, and in sixes; but seldom or never 
by tens. Man doubles, and triples, and quadruples; he di- 
vides into halves, thirds, and fourths ; but where does he 
estimate by ^ens or tenths, outside of arithmetic? There is 
nothing natural about the matter, except the fingers ; and 
these are grouped by fours instead of fives. 

Second, the decimal scale is unscientific. It originated by 
chance, by a mere accivlent. Had science, instead of chance, 
presided at its birth, we should have had a basis that would 
have given a new beaut}^ and a greater simplicit}^ to the 
admirable system of arithmetical language. 

Third, the decimal scale is inconvenient. This arises from 
the base, ten, not being divisible into the simple fractional 
parts, — third, fourth, and sixth. These fractions, which are 
in common use, cannot be conveniently expressed in the deci- 
mal scale, ih.Q fourth requiring two places, and the third and 
sixth giving interminate decimals. Were the basis of the 
scale twelve instead of ten, all these fractions could be ex- 
pressed in a single place. 

A Duodectinal Base. — The Duodecimal Scale would be 
much more convenient than the decimal. This is especially 
apparent in the expression of fractions in the numerical scale. 
In the duodecimal scale, we could express i-, ^, \, and i in a. 
single place, while ^ and ^ would require but two places. 
Thus, in the duodecimal scale, we should have |^=.6, -§^=.4, 
i.= .3, i-=.2, i=.16, and i=.14. The fractions -1- and | both 
give perfect repetends in the duodecimal scale, — thus, -|-=.2497 
and ^= .1864>35 ; but this would be no disadvantage, as these 
fractions are seldom used in actual life. The character <|> is 
used to express ten, for both teyi and eleven would be repre- 
sented by a single character in the duodecimal scale. 



334 



METHODS OF TEACHING, 



There seems to have been a natural tendency towards a 
duodecimal scale. Thus a large number of things are reck-- 
oned by the dozen; and the scale is even extended to the 
second and third degree, — to the grona and great gross. In 
our naming of numbers, the terms eleven and twelve seem to 
postpone the forming of a group until we reach a dozen. A 
similar fact is noticed in the extension of the multiplication 
table to "'12 times." The division of the 3'ear into twelve 
months, the circle into twelve signs, the foot into twelve 
inches, the pound into twelve ounces, etc., are further indica- 
tions of the same tendency. 

A change of our numerical base has been advocated. Leib- 
nitz preferred a binary base, and composed a binary arithme- 
tic. Charles XII. of Sweden seriously contemplated intro- 
ducing the duodecimal system into his dominions, and was 
probably prevented doing so only by his early death. If this 
change could be made, it would greatly simplify the science 
of numbers, and facilitate its applications. For a fuller dis- 
cussion of this subject, see Fhilosophy of Arithmetic. 

III. The Reasoning of Arithmetic. 

The science of aritlimetic, like geometry, embraces ideas and 
truths. These ideas give rise to definitions; and the truths 
are expressed in axioms and theorems or principles. The 
axioms are the self-evident truths that flow out of our numer- 
ical conceptions ; the principles are derived by reasoning. 
These principles may be applied in deriving methods of opera- 
tion and in the solution of practical problems. The statement 
of the method of operation gives us the rules of arithmetic. 

Definitions. — The definitions of arithmetic are concise 
descriptions of the ideas of the science. These ideas are of 
three different classes. First, we have our ideas of numbers 
as quantities ; as a unit, a fraction, a multiple, etc. Second, 
we have ideas of operation; as, addition, subtraction, etc. 
Tliird, we have ideas of relation; as, ratio, proportion, ale 



THE NATURE OF ARITHMETIC. 335 

The statement or description of these several classes of ideas, 
gives us the .definitions of arithmetic. The definitions of 
arithmetic are consequently of three classes ; definitions of 
Quantity, of Operation, and of Relation. 

Axioms. — The axioms of arithmetic are the self-evident 
truths which belong to the subject. They are of two classes; 
those which pertain to quantity in general and those which 
pertain to number in particular. Among the former are the 
following: "The whole is greater than any of its parts;" 
" Things which are equal to the same thing are equal to one 
another;" etc. Among the latter class of axioms may be 
mentioned the following: "Similar numbers only can be 
added;" "The multiplier is always an abstract number;" etc. 

The arithmetical axioms of the second class arise out of the 
particular conceptions of arithmetic. Each new conception 
of a relation or a process gives rise to one or more self-evident 
truths. Thus, as soon as we attain the idea of a factor as a 
maker of a number, we immediately perceive the truth that 
"a factor of a number is a divisor of the number." Also, as 
soon as we attain the idea of a multiple of a number as a 
number of times the number, we perceive the self-evident 
truth that "a multiple of a number contains the number." 

Jteasoning. — All reasoning is comparison. A comparison 
requires a standard, and this standard is t\xQ fixed, the axiom- 
atic, the known. The law of reasoning is to compare the com- 
plex with the simple, the theoretic with the axiomatic, the un- 
knoion with the known. By this comparison we pass from the 
simple to the complex, from the old to the new, from the known 
to the unknown. 

The reasoning of arithmetic is deductive. The basis of the 
reasoning is the ideas and self-evident truths, or the defini- 
tions and axioms. The definitions present the forms of quan- 
tity about which we reason ; the axioms present the truths 
which guide us in the reasoning process. With these as a 
basis we trace our way by comparison from the simplest truth 
to the profoundest theorem. 



336 METHODS OF TEACHING. 



Some writers hold that there is no reasoning in arithmetic, 
but that its operations and principles are the result of intui- 
tion or immediate judgment. This mistake arises from sup- 
posing that the science of arithmetic is contained in and 
grows out of addition and subtraction, which are regarded as 
purely mechanical processes. Comparison lies at the basis of 
arithmetic, unfolds the two primary processes, and gives rise 
to other processes not contained in addition and subtraction. 
The processes of reasoning in arithmetic can be reduced to 
the syllogistic form the same as in geometry. The demon- 
stration of principles in arithmetic can be made as logical as 
those in the science of form. Besides, if there were no reason- 
ing in ax'ithmetic there could be no science of arithmetic. 

Arithinetical Analysis. — One of the most common forms 
of I'easoning in arithmetic is that known as Arithmeticol 
Analysis. It is a process of reasoning by comparing num- 
bers through their relation to the Unit. Assuming that all 
numbers are so many times the single thing, they bear a 
definite relation to the unit which is immediately appre- 
hended. From this evident and simple relation to the unit, 
all numbers, integral and fractional, can be readily compared 
with one another, and their properties and relations deter- 
mined. The process is readily illustrated by solving the prob- 
lem, " If 3 times a number is 18, what is 5 times the number?" 
or, "Iff of a number is 30, what is 4 of the number?" 

This simple process of analysis runs through the whole 
science of arithmetic. It is its key-note; its basis principle. 
The Unit is the fundamental idea to which and from which 
we reason. It is a sort of arithmetical centre around which 
the reasoning process revolves, as the planets around their 
solar centres. The process is called analysis; but it t\-ill be 
noticed that it contains a synthetic element also. When we 
pass from a collection to the single thing, that is, from a 
vumher to the iinit^ the process is analytic; but when we pass 
from the unit to a numbei-, the process is synthetic. Both 



n 



TEIE NATURE OF ARITHMETIC. 337 

processes are inclufled under the more general term Compar- 
ison. Comparison is properly the thought process; Analysis 
and Synthesis are mechanical processes. 

The Equation. — The Equation lies at the basis of mathe- 
matical reasoning. The Equation is a universal form of 
thought, and belongs to arithmetic as well as to algebra. The 
simplest process of arithmetic, " One and one are two " 
(1-|-1=2), is really an equation, as much so as x'^-{-ax=h. 
The equation is an indispensable element of arithmetical 
reasoning; it is the key with which we unloclc the most 
complex problems of the science of numbers. • 

The equation in arithmetic assumes several different forms. 
Its primary form is that used in comparing two equal quan^ 
titles of different form ; as 2 x 3=6, in which 2 x 3 is one form 
of quantity and 6 another, the two equal in value, but involv- 
ing quite different conceptions. A comparison of unequal 
quantities gives us ratio, which may be expressed in the form 
of an equation; as 8 : 4=2. A comparison of equal ratios 
gives us an equation of relations, called a proporlion; as 
8 : 4=12 : 6, a proportion being in reality an equation. In 
arithmetical anal3'sis, an unknown number involved with 
known numbers is equated with known numbers; as "3 times 
a number equals 24." The treatment of the equation in 
arithmetic gives rise to transposition and substitution^ as may 
be seen in arithmetical analysis. 

That the equation belongs to arithmetic is thus evident. 
Every formal comparison between two quantities necessarily 
leads to it ; and such comparisons are continuall}' made. All 
of our reasoning involves it; we cannot think in arithmetic 
without the equation. The mind here takes its first steps in 
equational thought which, when continued, leads to the high 
places of mathematical science. Here the 3'oung mind plumes 
its wings to follow the great masters in their lofty flights in 
the regions of abstract thought, far be5^ond that to which the 
science of arithmetic could ever attain. 
15 



838 :^IETI{0DS OF TEACHING. mS^H 

Induction in Arithmetic. — Arithmetic is a deductive 
science, and most of its trutlis are derived by deduction. It 
is possible, however, to obtain some of its truths by induction. 
Upon seeing tliat a certain thing holds good in several cases, 
we may often correctly infer that it holds good in all cases 
and is a general principle. Thus the property of divisibility 
by nine may be presented to a learner inductively before he is 
able to understand a demonstration. The principles of frac- 
tions may also be derived inductively' from the examination 
of special cases. Indeed, many arithmetical truths were first 
discovered in this way and afterward demonstrated. The law 
that "every number is the sum of one, two, or three trian- 
gular numbers; the sum of one, two, three, or four quad- 
rangular numbers;" etc., has never been demonstrated except 
for triangular and square numbers, though it is known from 
induction to be perfectly general. 

The same method of reasoning is possible also in algebra. 
Newton's Binomial Theorem was derived by pure induction; 
the author left no demonstration of it, and yet it was regarded 
as one of his greatest discoveries and was engraved upon his 
tomb in Westminster Abbey. Legendre, in his Theory of 
Numbei's^ gives a formula for finding the number of primes up 
to a certain limit, wliich has never been fully demonstrated. 

Care mufet be exercised in the use of induction in mathe- 
matics ; some propositions derived by induction were subse- 
(luently found to be untrue. Fermat stated that the formula 
2wi_|_ I [^ alwaj's a prime when m is taken any term in the series 
1, 2, 4, 8, 16, etc.; but Euler found that 2^^+l is a composite 
number. Euler made a similar mistake in his formula for 
resolving the equation .r'+At/=B, whicli was detected by 
Lagrange. Some of the formulas for primes illustrate the 
same point. Thus, a:'^ -{- x -{- i gives primes for the first forty 
values of a; ; x'-i-j:-\-n, for the first seventeen values; and 
2j;'^-|-29, for twenty-nine of its first values. 



I 



TRf^ATMENT OF ARITHMETIC. 339 

lY. The Treatment of Arithmetic. 

The Science of Arithmetic is embi-aced in the three opera- 
tions, — Synthesis, Analysis, and Comparison. Synthesis and 
Analysis give rise to two classes of operations, distinguished 
as Primary and Secondary, or Fundamental and Derivative. 

I. Fundamental Operations. — The Fundamental Opera- 
tions include Addition, Subtraction, Multiplication, and Di- 
vision. They are called fundamental because the}' lie at the 
basis of all other arithmetical operations. 

Definitions, — Addition is the process of finding the sum of 
two or more numbers. Subtraction is the process of finding 
the diference of two numbers. Multiplication is the pro-, 
cess of finding- the product of two numbers. Division is the 
process of finding the quotient of two numbers. By using 
the terms product and quotient in defining multiplication and 
division, we secure a happy uniformit}' in the four definitions 
that has not heretofore existed. 

Cffses. — Each of these operations embraces two general 
eases: first, to find the results independently of the notation 
used to express numbers; second, to find the results of num- 
bers as expressed in written characters. The first case in 
each is a process of pure arithmetic, independent of any 
notation ; the second case in each has its origin in the Arabic 
system of notation. 

Treatment. — The two distinct cases require distinct meth- 
ods of treatment. In the former case, we operate on the 
numbers directly as loholes ; in the latter case, we operate upon 
them by parts. The first method is independent of any nota- 
tion ; the second method in each is developed by means of the 
elementary results obtained by the first method. 

We obtain the elementally sums by intuition; we obtain the 
elementary differences b}- intuition, or by an inference from 
the elementary sums; we obtain the elementary products by 
addition; we obtain the elementary quotients by successive 



3i0 METHODS OP TEACHING. 

subtraction, or by a reversing of the elementary jjroducts. 
These elementary results are used in obtaining the results 
with large numbers expressed in the Arabic system. A brief 
discussion of the philosophy of the methods of operation with 
the Arabic system is recommended. 

II. Secondary Operations. — The Secondary Operations are 
Composition and Factoring, Common Divisor and Common 
Multiple, Involution and Evolution. The new division, called 
Composition, seems necessary for scientific completeness, that 
each analytical operation may have its corresponding s^ni- 
thetical operation. It is also convenient in naming certain 
operations for which we formerly had no appropriate term. 

Definitions. — Gomposilion is the process of forming com- 
posite numbers out of the factors. Factoring is the process 
of finding the factors of composite numbers. A common 
divisor of two or more numbers is a number that will exactly 
divide each of them. A common multiple of two or more 
numbers is a number which is one or more times each of those 
numbers. It is usuall}^ defined as a number which contains 
these numbers, but this does not include the idea of multiple. 

Treatment. — In treating these subjects, we first establish 
some general principles, and then derive the methods of op- 
eration from these principles. It will be well to require the 
student-teacher to show the method of development of each 
division, and to point out the philosophy of the method of 
treatment. 

III. Common Fractions. — Integers originate in a s^'nthesis 
of units, fractions in a division of the unit. A fraction in- 
volves three things: first, a division of the unit; second, a 
comparison of the part with the unit ; third, a collection and 
numbering of the parts. A Fraction is thus a triune product 
— a result of analysis, comparison, and synthesis. A fraction 
ma}^ also arise from the comparison of numbers. 

Definition. — A Fraction is a number of equal parts of a 
unit. This seems to be an improvement on "one or more 



TKEATMEXT OF ARITHMETIC. 341 

equal parts of a unit." Since the parts of a unit are num- 
bered, these may be called fractional tinits, and a fraction 
may be defined as a number of fractional units. Among 
many of the incorrect definitions, we mention, — "A fraction 
is a part of a unit ;" " A fraction is an expression for one or 
more of the equal parts of a unit;" "A fraction is nothing 
more nor less than an unexecuted division." 

Cases. — The cases of fractions are all included under S^n- 
thesis, Analysis, and Comparison. To perform the synthetic 
and analytic processes, we need to change fractions from one 
form to another ; hence Reduction enters largely into the 
treatment of fractions. The comparison of fractions gives 
us several cases called Relation of Fractions. The student- 
teacher may state the cases. 

Treatment. — There are two methods of developing com- 
mon fractions, known as the Inductive and Deductive Meth- 
ods. B\' the Inductive Method, we solve each case b^^ analy- 
sis, and derive the rules by inference or induction. By the 
Deductive Method we first establish a few general principles, 
and then derive rules of operation from these principles. The 
Inductive Method is simpler for 3'oung pupils; the Deductive 
is more satisfactory for older pupils. The student-teacher 
may illustrate both methods. 

Principles. — The deductive method is based on certain 
principles which express the law of multiplying or dividing 
the terms of a fraction. These principles can be demonstrated 
either by the principles of division or independently as frac- 
tions. The latter method is by far the better. There should 
be a real demonstration, and not some loose statement such 
as we often find in arithmetics. 

ly. Co:mparison. — We have not room to indicate the treat- 
ment of comparison, but refer the student to the author's 
Philosophy of Arithmetic. A review of the subjects of arith- 
metic, pointing out. the philosophy of its methods of treat- 
ment, would be of adv^antaore to the student-teacher. 



34:2 METHODS OF TEACHING. 

V. The Course in Arithmetic. 

Arithmetic, for the purpose of instruction, ma}- be divided 
into two parts; Mental Arithmetic and Written Arithmetic. 
In Mental Arithmetic the problems are solved without the 
aid of written characters. In Written Arithmetic the opera- 
tions are performed with the aid of written characters. 

Oral Arithmetic. — Many educators divide the course into 
Oral and Written Arithmetic; and at first thought such a 
division seems plausible and natural. Language is of two 
kinds, oral and written ; when we solve problems without 
written characters it is naturally called oral arithmetic ; when 
the operations are performed with written characters it is 
naturally called written arithmetic. Such a division is, how- 
ever, a mistake, and results from a superficial view of the 
subject. Written Arithmetic is just as oral when recited as 
Mental Arithmetic ; and Mental Aritlimetic is no more oral 
when not recited than Written Arithmetic. Both are oral 
when recited ; neitiier is oral when not recited. 

Intellectual Arithntetic. — Nearly all authors of Mental 
Aritlimetic call their works Intellectual Arithmetic. The 
term Intellectual is, however, objectionable, as it does not 
accord with popular usage. No one thinks of calling a " men- 
tal solution" an "intellectual solution;" or would say, "he 
solved it intellectually," but rather, " he solved it mentally," 

Practical Aritlimetic. — Many authors call their works on 
written arithmetic. Practical Arithmetic. This, however, is a 
misnomer; all arithmetic should be practical, mental arithme- 
tic as well as written arithmetic. Tlie proper term is written, 
to indicate that we emi)loy written characters. The term 
" Practical" may do very well as a " trade mark " but it 
should not pretend to any scientific accuracy. It was sug- 
gested by Orontius Fineus, in 1535, in a work entitled Arith- 
metica Practica ; and first used by Joseph Chapman in 1732 
in a work entitled " Practical Arithmetic Compleat." 



TREATMENT OF ARITHMETIC. 343 

True Division. — The natural division of the subject is, 
therefore, into Mental Arithmetic and Written Arithmetic. 
There are several considerations in favor of the term Mental. 
First, it is in accordance with the popular usage, for all per- 
sons would say of a solution without the aid of written char- 
acters, " he solved it mentally," and not " orally" or " intellec- 
tuall3^" Second, the distinction is philosophical. Both meth- 
ods of solution employ the mind, and one employs the written 
characters also, and it is appropriate to distinguish the two 
methods by this distinguishing characteristic, calling that 
which employs written characters Written Arithmetic, and 
the other, which is purely mental, Mental Arithmetic. One is 
purely mental and the other mental and written^ and it is nat- 
ural and convenient to distinguish them by names which indi- 
cate these distinguishing characteristics. 

School Cotirse. — The common school course of arithmetic 
may be divided into two parts ; Primary Arithmetic and Ad- 
vanced Arithmetic. The Primary Arithmetic is designed to 
teach a child the elementary ideas and processes of arithmetic; 
the Advanced Arithmetic is designed to present as full a 
knowledge of the science as should be taught in our public 
schools. In some schools a course in Higher Ai'ithmetic may 
also be required, including the raoT'e abstruse principles of the 
science and a more extended application of them. 

Nnuiher of Boohs. — If mental and written exercises are 
combined after the Primary Arithmetic, the entire course may 
be embraced in two books, which may be called the Primary 
Arithmetic and the Union Arithmetic. If it is thought best 
to separate the mental and written exercises after the first 
book, we shall have three books in the course, which may be 
distinguished as the Primary Arithmetic, Mento,l Arithmetic, 
and Written Arithmetic. In schools of a certain grade there 
has been' a demand for a book between Primary and Advanced 
Arithmetic, whiclihas been met by an Elementary Arithmetic. 
Union Arithmetic. — Mental and written exercises should 



344 METHODS OF TEACHING. 

be combined in the Primary Arithmetic, and many teachers 
advocate this union througliout the entire course. The reasons 
are: 1. Economy of time; 2. Economj^ in the purchase of 
books; 3. One aids in learning the other ; 4. The sole object of 
Mental is to aid in the study of Written. The objections are ; 

1. Their object is different ; the object of Mental is discipline 
in analysis, the object of Written is skill in calculation ; 

2. Their spirit is diverse ; one being analytic and the other 
more syntltetic ; 3. They cannot be properly coordinated; 
4. Hence to combine is to neglect Mental. The present desire 
for combination is an example of history repeating itself, as 
may be seen in the works of Smith, Emerson, etc. Whether 
this demand will be permanent, or, like a new fashion, change 
again in a few years, time will decide. 

Extent of Course. — Many teachers tliink the present com- 
mon school course in arithmetic too extensive, but we doubt it. 
The child needs a thorough drill in arithmetic for the thought- 
power it imparts ; and for the practical value of arithmetical 
knowledge. Every child coming out of our public scliools 
should have a good practical knowledge of nearly every sub- 
ject treated in the ordinary common school arithmetic to 
prepare him for the practical duties of the business world. 

Course in Arithmetic. — We shall discuss the subject 
under three heads; Primary Arithmetic, Mental Arithmetic, 
and Written Arithmetic. These three parts are not entirely 
distinct ; to some extent they run into and overlap one an- 
other; but a clearer idea of the principles and methods of 
instruction can be given by such a division. The several sub- 
jects embraced in the course are as follows: — 1. Ideas of 
Numbers; 2. Arithmetical Language ; 3. Operations of Arith- 
metic ; 4. Reasoning of Arithmetic ; 5. Definitions of Arith- 
metic ; 6. Rules of Arithmetic ; 7. Principles of Arithmetic ; 
8. Applications of Arithmetic. In the next three chapters we 
shall consider tlie methods of teaching Arithmetic. 






CHAPTER III. 

TEACHING PRIMARY ARITHMETIC. 

rriHE course in Primaiy Arithmetic should embrace the 
JL Ideas of Numbers, Arithmetical Language, the Funda- 
mental Operations of Synthesis and Analysis, the Elements 
of Fractions, and the Elements of Denominate Numbers. In 
other words, the course should embrace the elements of 
Numeration and Notation, the elements of Addition, Subtrac- 
traction, Multiplication, and Division, the elements of Frac- 
tions, and the elements of Denominate Numbers. 

Principles of Teachim/. — In pi-esenting these subjects to 
the learner, it is believed that the course of instruction should 
be based upon the following principles : 

1. The fii'st lessons in arithmetic should be given by means 
of oral exercises. Such instruction is needed for several 
reasons: First, pupils can learn arithmetic before they can 
read ; and hence, of course, before they can use a book. 
Second, even with pupils who can read, such exercises are 
a very valuable preparation to the study of the subject in the 
text-book. Third, more thought can be developed, more in- 
terest awakened, and much more rapid and thorough progress 
can be made with such exercises. These exercises should be 
continued throughout the entire course in arithmetic. Every 
subject, even in the more advanced parts of written arith- 
metic, should be introduced by such exercises. 

2. The first lessons in Primary Arithmetic should be given 
by means of sensible objects. Such exercises will give distinct 
ideas of arithmetical quantities. Children's numerical ideas 
are often vague and indefinite. The names of numbers are 
often merely abstract terms to thorn. The denominations 
ounces, gills, pints, cords, etc., are often mere words without 

1'^* (345) 



346 



METHODS OF TEACHING. 



any concrete meaning to them. The ideas and processes of 
fractions cannot be clearly understood by children without 
such illustrations. 

The objects used may be marbles, grains of corn, beans, 
peas, little blocks, etc. Dr. Hill says the whole science of 
arithmetic may be taught with a pint of beans. The most 
convenient object for mau}^ of the processes is the Numeral 
Frame, or Abacus. This should l>e in every public school, 
and should be in constant use. Large ones, three or four feet 
sqiiare, are used in the primary schools of Sweden, Germany, 
etc. Many authors give pictures of objects, marks, stars, 
etc., in their books; but these do not seem to be necessary, 
as the objects themselves are better than the pictures of 
objects. Besides, no pupil should begin to study arithmetic 
in a text -book, who needs pictures to aid in the primary 
operations. 

3. In Primary Arithmetic^ the order of instruction is, — 
Jirst the viethod, then the reason for it; first the mechanical 
port, then the rational. This is the natural order of develop- 
ment with children; first the how and then the ichy. Methods 
of doing should be taught before the reasons for doing; ideas 
should be taught before the expression of them; operations 
before rules describing operations. Principles should follow 
problems ; not precede them. Much precious time has been 
wasted in primary instruction by the violation of this prin- 
ciple; and minds have been dwarfed by being led to incorrect 
habits of study and thought. 

4. In Primary Arithmetic^ the method of teaching should 
be inductive. The pupil should be led to each new idea and 
process by appropriate questions and illustrations. The defi- 
nition should be drawn from the ideas, rather than the ideas 
from the definition. The pupil should be led to see tlu> prin- 
ciple clearly before he is required to state it; and rules or 
methods should be derived by inductive inferences from 
analytic solutions. The child should be led to see the propri- 



TEACHING PRIMARY ARITHMETIC. 347 

ety of a, new term foi' the expression of a new idea, when pos- 
sible, for he will then see the meaning of it. 

5. Mental and Written Arithmetic should be united in Pri- 
mary Arithmetic. This is indicated by the logical relation of 
the subjects. As soon as the pupil can express arithmetical 
ideas orally, he is ready to learn to express them in written 
language. This combination is also a matter of practical con- 
venience. A pupil will learn more rapidly by having the two 
taught together. Each will throw light upon the other, and 
assist the pupil in understanding and remembering it. Men- 
tal and written exercises are mutually dependent in the pri- 
mary processes; the mental exercise prepares for the writ- 
ten, and the written aids the mental. They should, therefore, 
go hand in hand in primary instruction. 

Whether these exercises should be mixed along through the 
book, or whether they should be given separately, requiring 
the teacher to mix them in his instruction, is a question. As 
an abstract question, we believe it would be best to give them 
separately and have the teacher coml)ine them in his instruc- 
tion. With young and inexperienced teachers, however, it 
will probably be best for the text-book to unite the two kinds 
of exercises as the author thinks they should be naturally 
developed together. 

I. Teaching Arithmetical Language. 
Arithmetical Ideas. — The first step in the science of num- 
bers is the attainment of numerical ideas. The ideas of num- 
bei's originate in a succession of mental states constituting 
periods of time. With children the idea begins with the 
perception of objects, and is developed by a process called 
counting. The earliest ideas are usually learned upon the 
mother's knee, as she fondles with the little fingers, or num- 
bers the toys with which childhood beguiles the happy hours. 
Still, though a child may be able to count when entering 
school, an exercise for a fuller development of the numerical 
idea should not be omitted. 



3-18 METHODS OF TEACHING 

In counting, we should not rest satisfied with the mere 
naming of numbers in succession, for a child may do this and 
have no idea of the meaning of the words used. One, two^ 
three, etc, may be to it a mere succession of sounds, like do, 
re, mt, etc., without embodying any idea of collections. Chil- 
dren have been known to run off these words very glibly, even 
as far as a- hundred, without being able to select a dozen 
grains of corn from a collection. 

Children should be required to count with objects. The 
numeral frame is the most convenient, though other objects 
may be used. A counting exercise may be made lively b}' in- 
creasing and diminishing the number b}'' several at the same 
time. Little counting games with beans or grains of corn, 
will also be found intei-esting. Counting exercises should be 
continued until the pupils can count readil}^, and have definite 
ideas of numbers. If pupils can count when they enter school, 
these exercises need not be continued long. Pupils should be 
taught to count backwards as well sls forivards. This will be 
of advantage in learning to subtract, as we may " count off" 
to find a difference, as well as " count on " for a sum. 

Arithmetical Language. — Arithmetical Language is the 
method by which we express numbers. It is both oral and 
written; the former is called Numeration, the latter is called 
Notation. In teaching arithmetical language, Numeration 
should precede Notation. This appears from the fact that oral 
language comes before written language. This is a point which 
seems to have been overlooked by some writers, for they speak 
of " Notation and Numeration," as if the latter followed the 
former in the natural order. The reason for this mistake is 
that they restrict Numeration to the reading of numbers after 
they are expressed in figures. 

Numeration. — The oral language of arithmetic must be 
taught in connection with the development of the idea of 
number. The idea and the word are so intimatelj^ related 
that the former leads immediately to the latter; they are twin- 



I 



TEACHING PRIMARY ARITHMETIC. 349 

born, and go hand in hand in pure arithmetic. The names of 
numbers are, therefore, taught with objects and by means of 
counting. 

Two Methods. — There are two methods of teaching the 
names of numbers, which may be distinguished as the Com- 
mon Metliod and the Scientific Method. These two methods 
agree as far as ten. By the Common Method, we teach chil- 
dren to say eleven^ twelve^ thirteen^ etc., using the names after 
^671 just as arbitrarily as we do the names of the first simple 
numbers up to ten. The method does not indicate to the 
pupil the method by which numbers are named, — that is, the 
principle of grouping by tens. 

By the Scientific Method, when we reach ten^ we give the 
pupils the idea of a group, and then, instead of having them 
say eleven^ twelve^ etc., we require them to say one and ten, two 
and ten, thi^ee and ten, etc., up to ten and ten, which we show 
them consists of two groups of teu, and teach them to count tivo 
tens, two tens and one, etc., etc. After the pupils are familiar 
with these forms, we show them that these expressions have 
been changed into those in common use; thus, three and ten 
may be abbreviated by dropping tlie "and," changing </iree to 
//ijr, and ^en to <ee?i, giving thirteen; and similarly for the 
other names. 

The advantage of this method of teaching the names of 
numbers is, that it leads pupils to see the principle by which 
numbers are named which, by the ordinary method, is so con- 
cealed that it generally never occurs to their minds. It is 
also an excellent preparation for Notation, and greatly sim- 
plifies the task of teaching pupils to express numbers by 
figures. Some excellent teachers of primary arithmetic teach 
pupils to count by using one-teen, tivo-tecn, three-teen, etc., 
•also two-t}j one, two-tij two, etc., that they may see the law by 
which numbers are named. 

The groups ma}^ be indicated by the numeral frame, or by 
a little bundle of sticks, or by marks on the board enclosed 



350 METHODS OF TEACHING. 

by a circle. The grouping of ten tens for the hundred^ and 
ten hundreds for the thousand^ m^y also be explained and 
illustrated. The law of naming numbers beyond the thou- 
sand is best illustrated in connection with the writing of 
numbers. 

Notation, — When the pupils have acquired a little famil- 
iarity with the oral language of arithmetic, they are to be 
taught its written language. As soon as the}' have learned a 
few names of numbers, they should learn to express them in 
writt-en characters! A knowledge of the written language of 
arithmetic includes a knowledge of the characters and the 
method of combining them. We first teach the arithmetical 
characters to express the first few numbers, and then their 
combination to express the numbers above nine. 

The Characters. — We first give the nine digits^ and drill 
the children in naming and writing them until they are 
entirely familiar with these characters. If they have learned 
a little addition and subtraction, they may use the characters 
in solving simple problems, the teacher giving no problem at 
present which involves a number greater than ?n'/?e. Before 
the teacher explains the method of expressing numbers be- 
yond nine, it would be well to have the pupils try how they 
would express twelve, thirteen, etc., with the characters which 
they have learned. Their very failure will prepare them to 
appreciate the correct method when presented by the teacher. 

Combination of Characters. — There are two methods of 
teaching the combinations of the characters, or of teaching 
the written language from one to one hundred^ which may be 
distinguished as the Covimon 3fethod and the Scientific 
Ifethod. By the Common Method, we give the combined 
characters without explaining the principle of the combina- 
tion. Thus we teach that 10 expresses ten, 11 expresses- 
eleven, 12, twelve, etc., without any reference to tens and units. 
This is the method which is usually employed, and seems to 
be preferred to the scientific method. 



TEACHING PRIMARY ARITHMETIC. 351 

By this method, we would give the expressions for numbers 
as far as 20, and then drill the pupils in reading; and writing 
them until the}' were entirely familiar with them. We would 
next give the expressions from 20 to 30, and drill in like man- 
ner and thus continue as far as 100. After pupils are familiar 
with this method of writing numbers as far as 100, the teacher 
may show the pupils the principle of the combination, that 
the figure in the first place represents ones or units, in the 
second place tens, etc. When this is understood, we should 
require the class to analyze these expressions as follows : 
Analyze 2 5 (twenty-five). In 25, the 5 represents 5 units, 
and the 2 represents 2 tens. 

By the Scientific Method we explain the principle of the 
combination at the beginning. Having taught the pupils to 
count one and ten, two and ten, etc., we tell them that 1 placed 
at the left of another figure expresses a ten, and thus that 14 
expresses 4 units and 1 ten, or ''■four and ten;^' that 13 ex- 
presses 3 and 1 ten, or " thi-ee and ten,''^ etc. Finall}', they 
may be led to see that since 1 ten is expressed by a 1 in the 
second place, we need a character to express no ones in tlie 
first j)lace. We then tell them that we use the zey^o, 0, for 
this purpose, and thus represent ten 'by 10, which is 1 ten and 
ones. 

The latter of these two methods is preferable. It is more 
philosophical, for it shows tlie principle of the Arabic method 
from the beginning, which the common method conceals. It 
is more practical, for pupils will learn to write numbers much 
more readily by it than by the other method. Give the pupils 
a few examples to illustrate the principle, and they will be 
able to express the rest of the numbers up to 99 without be- 
ing shown by the teacher. Moreover, perceiving the princi- 
ple of 7>^ace Da?»e in the small numbers, they will have no 
difficulty in understanding it when applied to hundreds, thou- 
sands, etc. 

Higher Groxips. — After pupils are familiar with the naming 



352 



METHODS OF TEACHING. 



and writing of numbers up to ninety-ntJie, they should be 
taught that the next group consists of ten tens, and is called a 
/iM?2^re(Z, and that the 7i«nfZrecZs are expressed by a figure in 
the thii-d j^lace. They should then be drilled until they can 
read and write in units, tens, and hundreds. The}^ should 
then be taught that a group of ten hundreds is called a thou- 
sand, that thousands are expressed by a figure in the fourth 
place. 

They should then be shown that the law of giving a new 
name for each higher group of tens is changed to giving a new 
name for each third group ; and that the intermediate names 
and places are tens and hundreds of the old group. "Up to 
this time the numeration has preceded and led the notation 
in the order of teaching ; after this it will be more convenient 
to invert the order, and let the notation lead the numeration. 
Numeration will thus be regarded not only as a method of 
naming numbers, but of reading them when they are writ- 
ten in Arabic characters. 

Numerical Periods. — The pupils may then be taught to 
separate written numbers into numerical periods, and to 
name and remember the periods. Perpendicular 
lines may be drawn, and the columns headed 
units, tens, etc., and the pupil be drilled in writ- 
ing numbers by putting the terms in the proper 
column. Such an exercise is not of much value 
if the teacher knows how to teach by the method previously 
suggested. The pupils should be drilled in reading and writ- 
ing numbers until they are entirely familiar with the subject. 
Do not hurry over the subject; haste here is "bad speed." A 
thorough knowledge of Numeration and Notation will remove 
the usual difficulties of the fundamental rules. 

This instruction in reading and writing the larger numbers 
should be presented gradually, in connection with the exer- 
cises in the fundamental rules. Do not keep the pupil at it 
until he has mastered it, but go on with adding and subtract- 



H. 


T. 


u 


3 


5 


~v 


6 


3 


8 


5 





6 



TEACHING PRIMARY ARITHMETIC. 353 

ing, etc., returning to the notation and numeration every clay, 
thus keeping up a constant review, and adding a little to what 
has been previously given, as the pupils are ready for it. The 
student-teacher will now give a model lesson in teaching 
arithmetical language. 

II. Teaching Addition and Subtraction. 

As soon as pupils have the ideas and names of numbers, 
and can 7^ead and lurite them, the3'" should begin to unite and 
separate them; that is, perform the processes of Addition and 
Subtraction. 

Principles of Teaching. — Instruction in these processes 
should be given in accordance with the following principles : 

1. Addition and Subtraction should be taught simultan- 
eously. This is indicated by the logical relation of the sub- 
ject. Subtraction is the converse of addition, and the 
elementar}' differences should be derived from the elementary 
sums. Thus, as soon as the child sees that 3 and 2 are 5, he 
is readj^ to see that 5 less 2 is 3, or 5 less 3 is 2. Thus, also, 
in finding the difference of 9 and 5, instead of counting 5 off 
from 9 to see what remains, he should infer the difference by 
knowing that 4 and 5 are 9. The synthesis of numbers in 
obtaining the sura should, therefore, be accompanied by the 
analysis of numbers in finding the difference. 

This method will be found to be especially convenient in 
practice. Taught in this way, the pupil will learn the ele- 
mentary differences while he is learning the elementary sums. 
He will thus not need to commit a Subtraction Table, which 
seems almost a necessit3- if subtraction is taught separately 
from addition. Knowing the elementary sums, if he has been 
taught to derive the differences from the sums, he can imme- 
diately obtain a difference without resorting to a table. 

2. Addition and. Subtraction should be taught by means of 
seyisible objects. Tliis is indicated by the nature of the sub- 
ject and the mind. It is the way in which the pupils reall}' 



354 METHODS OF TEACHING. 

must attain the sums of numbers, if the}' are to understand 
them. So strong is this necessity that, if the teacher does 
not require pupils to use objects, they will themselves use 
them by counting their fingers or using marks on the slate or 
blackboard. What the pupils do by nature, the teacher 
should require to be done upon principle. They should be 
required to see the sums before they say them. The most 
convenient object for this purpose is the numeral frame. 

The teacher should be careful, however, not to allow the 
pupils to use objects too long in adding and subtracting. 
They should be led from the concrete to the abstract, from 
seeing sums and differences, to thinking them. The habit, in 
pupils of nine or ten 3rears of age, of counting the fingers or 
using strokes, shows poor teaching; and the practice should 
not be allowed. 

3. Pupils should he required to commit an addition table. 
The neglect of this is very common, and the result is that 
very few pupils are ready in adding. It is not an unusual 
thing to see pupils who are entirely familiar with the multi- 
plication table, using strokes or counting their fingers in solv- 
ing simple problems in addition and subtraction. There is 
the same reason for committing an addition table as there is 
for committing a multiplication table. Pupils should be re- 
quired to viake and study an addition table. They should 
write it on the board, that seeing it may aid to fix it in the 
memory. 

Course of Lessons. — The course of lessons in Mental Addi- 
tion and Subtraction is as follows: 

1. Teach the pupil to increase and diminish by ones as far as 12 and 1, 
or 13. 

2. Teach the pupil to increase and diminish by ticos as far as 12 and 2, 
or 14. 

3. Teach the pupils to increase and diminish by thi-ees as far as 12 and 
3, or 15. 

4. Teach tlie pupils to increase and diminish hy fours, by f res, hy sixes, 
etc , up to 12 and 12, or 24. 



TEACHING PRIMARY ARITHMETIC, 355 

5. Have the pupils write these su7ns and differences in a table and 
study and recite them. 

6. Teach them to increase a number greater than 12 bv 1, 2, 3, etc. 
Thus, since 14 and 5 are 19, 21 and 5 are 29, etc. Also to diminish in 
a similar manner. 

Model Lesson. — Teneher, taking one book in his hand, asks, How manj' 
books have I in my hand? Pupils. One book. Teacher, taking another 
book in his hand, aslcs, How many books have I now? P. Two books. 
T. How many then are one book and one l)ook ? P. Two books. T. 
How many then are one and one ? P. One and one are two. T. How 
many books have I in my hand? P. Two books. T. 1 will take one 
book away; how many books have I now? P. One book. T. One book 
taken from two books leaves how many books? P. One book. T. One 
from two leaves how many ? P. One from two leaves one. Continue 
this exercise, and apply it also to two, three, etc. 

l*i'<ictlc<d E.icercises. — Tlie following exercises will be 
found valuable in teaching pupils to add and subtract with 
readiness and accuracy. Frequent drill upon such exercises 
is recommended. 

First E.rercise. — The teacher will name two numbers and require the 
pupils to give first their sum, and then their difference; thus, the teacher 
says. "5 and 2 ?" Pupils. "5 and 2 are 7, and 2 from 5 leaves 3." After 
a little practice thej^ may omit naming the numbers, and merely sa}', "The 
sum is 7, the difference is 3;" or "7, 3." To vary this, the boys may give 
the sum, and the girls the difference, and vice versa; or, if the class is 
all of one sex, a division may be made, one part giving the .mm, and the 
other the difference. In this and the following exercises, care should be 
taken that small numbers be used at first, until the pupils attain the 
ability to use larger numbers with ease and readiness. 

/Second E.tcrclse. — The teacher will select some number, and then give 
one part of this number and require the pupils to give the other part. 
Suppose 8 to be the number ; the teacher says "fice," jiupils answer, 
"three;" teacher, "two," pupils, "six," etc., etc. 

Third Exercise. — The pupils should also be required to add by twos, 
threes, etc, merely naming the results, as follows : 2, 4, 6, 8, etc., 3, 6, 9, 
etc., until the additions can be readily given. Begin also with one, and 
count by twos, thus : 1, 1^, 5, 7, etc.; also at 1, and count by threes, thus: 
1, 4, 7, 10, etc.; also at 2, thus: 2, 5, 8, 11, etc.; continuing the addition 
as far as it may be thought desiral)le. 

Let the pupil in a similar manner add hy fours, fires, r-tc, up to tweloes. 



1 


1 


2 


2 


3 


3 


4 


4 


5 


5 


(5 


6 


7 


7 



oO() METHODS OF TEACIIIXG. 

Such exercises should be continued day after day, in connection with 
the lessons which precede and follow this lesson, until great facility ig 
acquired in the operations. 

Fourth Exercise. — Give a pupil a number and require him to separate 
it into two parts; then into ^/wee parts, etc. Thus 6=3-}- 3 ; 6=^4+2; 
6=35+1. Also 6=2+2+2;'6=4+l+l; 6=3+1+2 ; etc. 

Fifth Exercise. — Let the teacher write two columns of figures on 
the board, as indicated in the margin. Call the first column 
additive, and the second suhtrnctim. The teacher then with the + — 
pointer will indicate the number, the operation being indi- 
cated by the column. When he points to a figure in the first 
column, the number which it indicates will be added, but when 
he points to a figure in the second, the number indicated will 
be subtracted from the result which the pupils have pre- 
viously obtained. If the Arabic characters have not been 
given, numerical words may be written in columns, instead of q n 
the figures. 

These exercises may be conducted sometimes in concert and sometimes 
singly. While one is adding alone, let the others keep careful watch for 
errors ; a good degree of interest may thus be created, each pupil trying 
to obtain the largest sum before making a mistake. 

Written Addition. — While the pupils are learning to add 
and subti'act mentally, they should also perform work on the 
slate and blackboard with written characters. These exer- 
cises should hrst extend as far as the elementarrj smns, that 
is, to about " 12 and 12 are 24." So far written addition and 
subtraction should go together with the mental exercises ; but 
subsequently it is more convenient to separate theiD, teaching 
first addition and then subtraction. 

Cases, — Written Addition should be presented in two cases ; 
first, where there is nothing " to carry ;" and second, where 
there is something to carry. In both cases, we should first 
require the pupils to learn to peiiorm the operation without 
giving any reason for it. The primary object is to make them 
familiar with the mechanical operations. Subsequently they 
may learn to explain the work. 

Course of Ijessous. — The course of lessons in Written 
Addition is as follows : 



TEACHING PRIMARY ARITHMETIC. 357 

1. To write the elementary sums of the addition table. 

2. To add single columns of numbers, in which the sum exceeds nine. 

3. To add numbers of two, three, four, etc, terms, in which tlicre la 
nothing to carry. 

4. To add two columns in which there is something to carry, then 
three columns, etc. 

Ex pi a nation I. — The exphination may be given in what is 
called the Simple Form or in what is called the Full Form. 
By the Simple Form, the pupil will merely state the method 
without giving the reason for it. By the Full or Complete 
Form, the pupil gives the logical solution, which states each 
step in the process and the reason thereof. Young pupils 
should use the simple form, as they are not prepared to 
understand and state the reasons for the various operations. 
Much time has been wasted, and many youthful minds injured, 
by the attempt to have children give logical forms of explana- 
tion before they were prepared for them. With more ad- 
vanced pupils, we should require full explanations, in concise, 
simple, and logical language, showing the reason for every 
step of the process. For the two forms, see the author's 
Primary and Elementary Arithmeiics. The student-teacher 
will illustrate the subject in model lessons. 

Written Subtraction. — After the pupil is somewhat 
familiar with Written Addition, he should begin Written 
Subtraction. The subject should be presented under two 
cases: 1st, To subtract without "borrowing;" 2d, To sub- 
tract b}^ "borrowing." The first of these cases should be 
taught before the pupils take the second case of addition; 
the second should follow the second case of addition. The 
pupil should be first taught the mechanical method of doing 
the work, without being shown the reason for it or being re- 
quired to give any explanation of the process. A general 
idea of "borrowing" 10 from the next term of the minuend, 
and "carrying" 1 to the next term of the subtrahend, may 
be given to pupils who seem 2)repared to understand it ; but 
no logical solution should be required at first. 



)8 



METHODS OF TEACHING. 



Course of Lessons. — The course of lessons in Written Sub- 
traction is as follows : 

1. To write the elementary differences of the subtraction table. 

2. To subtract numbers of two, three, etc. terms, when there is 
notliing " lo Ijorrow." 

3. To subtract numbers of two terms, then of three terms, etc., when 
there is somelliing "to borrow." 

4. To subtract wlien there are two or more cipliers in the minuend. 
Ill list rat ion. — Tlic method of subtraction may be illus- 
trated by bunches of little sticks, representing tens, hundreds, 
etc., and showing how one bunch of a higher denomination 
represents ten of a lower, and how we can " borrow" one of 
the higher and unite it with the lower denomination. Little 
heaps of pebblgs, or of beans, or of grains of corn, and boxes, 
real or imaginary, may also be used, or pictures of them on 
the board representing the same. These may be of some aid 
to the beginner; but if the notation lias been thoroughly 
taught, there will be very little need of concrete illustration. 
Let the student-teacher give a lesson on the subject. 

Ejcplanation. — Young pupils should first be taught to do 
the work, and afterwards be required to ex[)lain it. The ex- 
planation should at first be in a simple form, merely indicating 
the steps of the mechanical process. Older pupils should 
give a full logical explanation. There are two methods of 
explaining the second case, known as the "'method of borrow- 
ing" and the "method of adding ten," either of which may 
be emplo3'ed according to the preference of the teacher. It 
is difficult to decide wliich is the simpler, though teachers 
generally prefer the method of "borrowing;" and when there 
are no ciphers in the minuend, it is probably the simpler. 
When tliere are several ciphers in the minuend, the method 
of "adding ten" is simpler. The latter method is much pre- 
lerred in practice. We should teach a pupil to subtract, in 
practice, bj'^ adding ten to the upper term, and adding one to 
the next higher term of the subtrahend, though many pupils 
are practising the opposite method at the present day. 



TEACHING PKIMARV ARITHMETIC. S50 

III. Teaching Multiplication and Division. 

As soon as the pupils arc somewhat familiar with addition 
and subtraction, they should begin multiplication and division. 
The old way of teaching multiplication was to begin l)}^ put- 
ting a "table-book" in the hands of the pupils, and requiring 
them to commit the multiplication table. What the table 
meant, where it came from, what it was for, or where it was 
going to or going to lead them, they knew no more than the}"" 
did of the origin or nature of a sunbeam. 

Principles of Teaching. — There is a better, easier, and 
more natural way; and this way we will suggest in the follow- 
ing general principles: 

1. Multiplication should be taught as concise addition. 
Thus the pupil should be taught that two 2's are 4, because 
24-2=4; or that two 3's are 6, because 3 + 3=6, etc. Instead 
of the pupil's entering upon multiplication as a new and in- 
dependent process, he will thus see the nature of the subject 
and its logical evolution from a general synthesis. He will 
seethe origin and meaning of the multiplication table; and 
not regard it as a mere collection of abstract names and num- 
bers to be committed to memory. He will be able to make 
the multiplication table for himself, and will see the reason 
for committing it to memory, that he may not have to derive 
the products every time he wishes to use them. 

2. Division should be taught as reverse multiplication. 
Division can be taught in two ways; as concise subtraction, or 
as reverse multiplication. That is, the elementai-y quotients 
may be obtained by a process of subtraction, or by reversing 
an elementary product. Thus, if we wish to show a pupil 
how many times 4 is contained in 12, we can subtract 4 suc- 
cessively from 12 three times to exhaust 12; and thus infer 
that 4 is contained in 12 three times. We can also derive the 
quotient from the consideration that, since three 4's are 12, 
12 contains three 4's, or 12 contains 4 three times. 



MIO 



MKTIIODS OF 'I'KAt IllNd 



IJotli of t lu^sc mct-liods ;\fc li>nil,imM.t(', bill, tlic iiidliod <>(" 
I'cvcrsc iiiiill ipliciit ion is pi'd'ci-riMl I'oi- Iwo itmsoiis. Fiist,, it 
is (lie iiioif coiivciiiciit ill pr:i(M,it'i', since tiiu rJcmaii/ari/ 
ijiiol ii'iil^ v:\\\ be iiiinirdiiiicly (Uirivcd I'loiii Uic clemeulary 
lifii(hic/.<:. I>y Uic iiicUkkI of (roiicisc siihLrucLioii, W(! slioiild 
liiivc l(> derive e;ieli eleiiieiil ;u y ([iiolieiil. by pefforininji^ S(!vcrill 
siibl nudjoiis, wliieli would ol'leii bi^ very ledioiis. Second, it 
iivoidH the n(^(U'ssily of conimiU iiit!,' :i, division (able. If Ave 
derive the eleiiient;iry (inolieiits by siilttraclioii, it would lie 
iieeessjiry to jirraiiij,*' them in a, table and eoininit lliein, as we 
do I he elementary products; but if we obtain the cpiotitMits 
by reverse mull iplieatioii, we can derive them Croiii the mul- 
t.ipliealion table, and will not need any table of dixisiiui. 

;}, J\li(lliii/ic(i/i()ii and Division s/ioiihl be. Iau(j/il, Kiinid- 
lancousli/. This is suij^^csted by the ]oj>;i(T!il relation of the 
two suliJeelMS. 'The two ideas are so iiil iinalcl\- related that 
one <j,"rows directly out, ol' the other. I'jVery synthesis sng- 
U'estH naturally its ojiposil-e, an nnalyHis. A uiiiltiplientive 
synthesis can hardly be made without the intimation of its 
opposite, a divisional i\(' analysis. 'I'liiis, as soon as the pu|)il 
learns that /o'/r liiiics Jirc (trc lirciih/, lie is prepared to see 
that. Iirciih/ contdins Jitu^^/'oiir tiim's. The inethoil siiii'm'sted 
is thus founded upon and indi(!at(Ml by the laws of tIiou!j,h|,. 

It is also iiiucli more convenient t,o present the subject in 
this manner. The same liu^t, a product, answers a. double 
])nrpose; tlH> additive process which determines a product, 
i^ives also the materials for a, ipiot ieiit . I n |iiact ice wi- should 
have the pupil commil- I he w hole of " one columir' of miilti- 
plieaiioii before wc lia\i' them derive the (piotieiits. This 
principle applies lo mental mult iplitvition and division, and to 
(he simple written exercises which repres(>nl, I hese operations, 
in wrillen mull iplieatioii and liivisioii proper, it is more con- 
venient to (each the pr()(!ess(>H Hei)arati'ly. iMulti|)lical ion 
should be tauii,lit first , and after the pujiils are (piit»' familiar 
with the process, t hey should pass t,o division. 



TEACHING PRIMARY AKITIIMKTIC, 30 1 

Malt i plication Table. — The Multiplication Table is a table 
of the elementary products. These products have to be com- 
mitted to mcMnory. This is not an easy task; indeed, it is 
one of the most diflicult tasks with which the young pupil 
meets. It requires months and sometimes years for the child 
to become thor()uj2;hly familiar with it. In the early history 
of arithmetic in Europe, operations were often performed in 
such a way as to require only a portion of the multiplication 
table, on account of the extreme difficulty of committing the 
products to memory. 

How shall we teach a child the table? The method of for- 
mer times is not easily forgotten. The book was put into 
the child's hand, and sometimes the birch upon his back, 
that the products might be put into his head. Who does not 
remember the toil and the trouble ; how we dreaded the result 
of* a treacherous memory ; how we rejoiced in " five times " 
and " ten tiines ;" how we " stuck" on " 9 times t," and '' T 
times 8," and confounded " 11 times 11," and " 11 times 12;" 
and how, at last, through great tribulation, we scaled the 
mount and stood victor of a hard-fought battle at the top? Is 
there a better way than the old way? 

The Method. — First, pupils should make the multiplication 
table for themselves. They will then see the nature and use 
of such a table, and will stud}- it with more interest and com- 
mit it with greater ease. Second, when thus formed, study, 
recitation, frequent repetition, are necessary to fix it in the 
memory. Tlie pupil must repeat it over and over, and be 
drilled upon it until he knows it. Tliird, writing it frequently' 
on the slate or blackboard, will assist tlie pupil in committing 
it to memory. The seeing of it will tend to lix it upon the 
visual memory, which is often better than attempting to fix it 
in the oral memory. The eye will aid the ear in making the 
accjuisition. Fourth, reciting the table in concert will also aid 
in learniugit. It gives animation and zest to the recitation, 
and deepens the impression through the increase of interest. 
16 



362 METHODS OF TEACHING, 

The duller pupils will thus learn also from the brighter pupils. 
The frequent hearing of the names associated together will at 
last make a permanent connection between the factors and 
the products, so that as soon as we think of one, the other 
will occur to us. Fifth, the singing of the table to a little 
tune is also recommended. This has been practiced by many 
teachers, and with good results. It is a pleasant exercise, and 
the pupil is learning a lesson while amusing himself with a 
song. There are several little tunes to which the words may 
be fitted; among the best is one known as "Sparkling Water," 
or " Old Dan Tucker," a coarse name for a beautiful mclod3\ 

Division Table Should a division table be committed to 

memory- ? It has been the custom of man}'' teachers to have 
their pupils study and commit a table of quotients after they 
have committed a multiplication table. This, however, is not 
necessary, if division is taught as reverse multiplication. 
The multiplication table gives also the quotients, the product 
being regarded as the dividend, and the two factors as divisor 
and quotient. If, however, division be taught as concise sub- 
traction, it will be necessary for a pupil to commit a division 
table, as he has no method of determining a quotient but b}^ 
subtracting, or remembering it from a table. 

Course of Lessons. — The course of lessons in Primary 
Multiplication and Division is as follows: 

1. Lead the pupil to a clear idea of "times," and then of a number 
taken several times. 

2. Lead the pupil to make the table of "two times," and have him 
commit it. 

3. Apply the table of "two times," in solving little problems like "If 
one orange costs 3 cents, what will 2 oranges cost?" 

4. Lead the pupil to derive quotients from "two times," and to apply 
these quotients to solving little problems. 

5. Proceed in the same way with "three times," " four times," etc., 
up to " twelve times," deriving the quotients from each multiplication 
column. 

6. Drill the pupils on writing and reciting the multiplication table 
until they have committed it. 



TEACHING PRIMARY ARITHMETIC. 3G3 

Jfj.id Lesson .— How many t lines do yon recite in a day? How many 
ti ji.cs does llie clock strike :it six '? If you have 2 cents in one liiuul and 
2 cjnts in tlu; olh^r li.ind, how niaay times 2 cents :iave yoii .■' How 
many CL-nts have you Z How many cents then are two times 2 cents.' if 
1 move ;5 bails over on this wii'c of the numeral frame, and then move 
three balls more, how many times 3 balls have I? How many balls in 
all .' How many then are two times 3 balls '! Write 4 on the board and 
then write 4 under it. How many times have you writ- 
ten 4? How many are 4 and 4.'' How many then are ;■«'« 2x1=3 

2x2=4 
times 41 Proceed in a similar manner up to 2 times 12. 9x3 = 6 

Then have them write the multiplication table on the board, £ x 4= 8 
usinji; the signs X iind = as in the margin. When the etc. etc. 
pupils know the jyroducts of "2 times," reverse ihe process 
for the quotients, thus : How many 2'smake 4? 4 then is how many 2's? 
4 then contains how many 2'sV 4 then contains 2 how many times? 2 
then is contained in 4 how many times? Proceed in a similar manner 
with the other quotients drawn from "two times." Then have the 
division table written on the board, using the symbols -:- and =. 

After the pupils are familiar with the process of deriving the multi- 
plication table by addition, lead them to see that they can obtain the 
successive products by increasing the last product by the number multi- 
plied to lind the next product. Thus, when they have "G times 4 are 
24," ihey can obtain 7 times 4 by adding 4 to the 24, making 28, etc. 
Many pupils will see this for themselves; those who do not should be 
led lo see it by the teacher. 

Practical Exercise. — To make pupils rapid and acctirate 
in the mechanical processes of adding, subtracting, multiplj-- 
ing, and dividing, the fulloAving exercise is practiced b}- some 
teachers, with excellent results : 

Let the teacher write four columns of figures on the blackboard, as is 
represented in the margin, the first column be- 
ing additive, the next subtractive, etc., as is in- 
dicated bj' the s\'mbols i)laced above them. The 
teacher, with the pointer, will point out certain 
figures, the corresponding numbers being added, 
subtracted, multiplied, ordivided, as is indicated 
by t)ie symbol at the head of the column. Care, 
of course, must be taken not to reri^uire a division 
by a number that is not exactly contained. This 
exercise may be coninued for many recitations, 
in connection with the other lessons, with great advantage to the pupils. 



-f) 


(-) 


(X) (--) 


1 


1 


] 1 


2 


2 


2 2 


3 


3 


3 3 


4 


4 


4 4 


5 


5 


5 5 


G 


G 


6 G 


7 


7 


7 7 


8 


8 


S 8 


9 


9 


9 9 



'dG\. METHODS OF TEACHING. 

Written Multiplication. — The pupils should write the 
elementary products and quotients as they are learning them. 
When they are familiar with the table, they are ready to learn 
written multiplication and division, properly so called. These 
should be taught separately, like written addition and sub- 
traction. We should begin with multiplication and drill the 
pupils upon it until they are quite familiar with the process 
of multiplying. 

Course of Lessons. — The subject should be presented in 
two cases ; first, when the multiplier does not exceed twelve^ 
and second, xvhen it does exceed tioelve. These two cases will 
include the following classes of problems: 

1. Write the elementary products in the usual form of written multi- 
plication. 

2. Multiply when the multiplicand consists of several terms, but not 
requirina; any "carrjing;" as, 214 multiplied by 2. 

3. Multiply when the multiplicand consists of several terms, the mul- 
tiplier being one term, and the products require "carrying," as, 3G8 by 2. 

4. MuUiply when there are two or more terms in the multiplier; as, 
457 by 23. 

5. Multiply when there are one or more zeros in the multiplier. 

6. Multiply when there are one or more zeros at the right of either of 
both multiplier and multiplicand. 

Explanation. — The pupils should first be required to do 
the work without giving any explanation of the process. 
When they have become familiar with the operation, they 
may be required to state the ditferent steps of the process 
without giving the reason for the same. This is what is called 
the sm;j/6\/br??i. of solution. Advanced pupils should be re- 
quired to give a full logical solution, in which the reason for 
each step is logically stated. For the simple form, see the 
author's Primary and Elementary Arithmetics; for the full 
solution, see the author's Written Arithmetic. 

Written Division. — The first lesson in written division 
consists in writing the elementary quotients as they are learned 
iu.the mental exercises; when he is familiar witli these, he 



TEACHING PRnfARY ARITHMETIC. 365 

may take up written division proper. The fundamental prin- 
cii)Ie in teaching written division is, that ahort and long 
division should be taught together, almost from the beginning. 
Let the pupils see that tliey are merely different waj-s of writ- 
ing the results. It will be well even to have him express the 
elementary quotients by both methods. This will avoid the 
difficulty that pupils usually experience in making the transi- 
tion from "short" to "long" division. 

Course of Lessons. — The difficulty of teaching written di- 
vision will be greatly lessened by a careful grading of the 
exercises. 

1. Express the elementary quotients. 

2. When there are several terms in the diviclend and quotient, but 
When there are no remainders; as, 248 divided by 2. 

3. When there are remainders, the divisor still not exceeding twelve ; 
as, 17 divided by 3. 

4. When tlie divisor exceeds twelve; as, 156 divided by 13. 

5. When there are one or more ciphers in the quotient; as, 3456 di- 
vided by 33. 

6. When there are ciphers at the right of the dividend and tlien attlie 
right of the divisor, and then at the right of both. 

In the first three classes, the problems should be solved by 
both "short" and •' long" division. In the fourth class, we 
must solve by " long" division. The divisors should be graded, 
beginning at 13, and passing on to 14, 15, 16, IT, etc. The 
difficulty which will now be met by the pupil is to ascertain 
the terms of the quotient. The teacher must lead him to test 
his quotient terras by the following considerations : 

1. The pupil will notice that there are four steps in the operation ; 
1st, Divide ; 2d, Multipli/ ; 3d, Subtract; 4th, Brinr/ doini. 

2. If, when we multiplj', the product is greater than the partial divi- 
dend, the quotient term is too large and must be diminished. 

3. If, wlion we subtract, tlie remainder is not less than tlie divisor, 
the quotient term is too small and must be increased. 

Explfiitatuni. — As in multiplication, the pupil should be 
required to do the work at first without giving explanation 
of the process. He should afterward be required to state the 



866 METHODS OF TEACHING. 

steps of the process -without giving the reasons for the steps. 
When he is sufHciently advanced, he should be required to 
give a full logical solution, such as is found in the author's 
arithmetics. 

The Gi'uhe 3IetJio(l. — There is a method of teaching- 
Primary Arithmetic extensively used in Germany, and highly 
recommended by a number of American educators, called the 
.Gruhe Method. The principle of this method is, that it 
makes each individual number, instead of the operational the 
basis of the instruction ; and combines in each lesson, from the 
start, the four fundamental operations. Thus, in treating the 
number 2, "all the operations possible within the limit of this 
number" are performed in the same lesson. Thus, the child* 
is taught that 1 + 1 = 2,2x1 = 2,2 — 1 = 1,2-7-1 = 2, 2-=-2=l, 
etc. In teaching the number 4, the lesson is l-j-l + l + l = 4, 
4 — 1 = 3, 4x1 = 4, 4^1 = 4; 2 + 2=4, 2x2=4, 4 — 2=2, 
4-~2=2; 3+1 = 4, 4—3=1, 3x1 + 1 = 4, 4-t-3=1, and 1 re- 
maining, etc. The Avhole circle of operations is exhibited and 
taught in treating each iudividual number. 

Against this method we enter an earnest protest. It is 
false in philosophy and tedious and i)erplexing in practice. 
Its adoption by any intelligent teacher iu this country can be 
explained only by its novelty, or a lack of experience in 
teaching primary- arithmetic. The objections to it are funda- 
mental. It requires the pupil to grasp four diverse funda- 
mental operations — addition, subtraction, multiplication, and 
division — in the ver^^ first lessons of arithmetic, which is in 
contradiction to the simplest principles of the mental growth 
of a child. It is false in philosophy, as it makes iiumher the 
basis of instruction, instead of the operations upon number. 
It is inconvenient in ])ractice; to be of any practical ad vr.n- 
ttige. it should be continued as far as 144, the limit of the table 
of elemen.tary products and quotients, or at least to 81, the 
product of 9 times 9; which would require years of labor to 
attain that which a child can easily derive for itself when it 



TEACHI2CG PRIMARY ARITEIMETIC. 307 

is familiar with the nature of the fundamental opei'ations, and 
has acquired the elementary sums and products. 

The Grube method inverts the order of arithmetical thought 
and development, puts analysis before synthesis, when ac- 
cording to the very genesis of number, from the one to the 
many, synthesis should precede analysis. "Wc should learn 
that 2 and 2 are 4 before we begin and -separate 4 into its 
elements; or that 6 times 8 are 48, before we separate 48 into 
6 times 8. The child must learn, commit to memory, the 
elementary sums and differences as given in the "addition 
table;" and the elementary jjroducts and quotients as con- 
tained in the " multiplication table;" and with these he can 
make all the analyses of the Grube method for himself. But 
tlie Grube method inverts all this and assumes that the child is 
in some wa3' or another to reach these elementary sums, differ- 
ences, products, and quotients, b}' the long and tedious pro- 
cess of analyzing the different numbers in their order from ] 
to some limit, 100 or 144. 

A simple comparison of the Grube method with a clear 
conception of the ordinary method, it would seem, should 
be sufficient to prohibit its use in the first lessons of arithme- 
tic. We recommend exercises similar to those of the Grube 
method, but they should follow and not precede the learning 
of the elementary sums, differences, j^f'odu-cts, and quotients. 

lY. Teaching Common Fractions. 

After the pupils are somewhat familiar with the funda- 
mental operations, they are ready to begin the subject of Com- 
mon Fractions. In teaching Fractions, the teacher should be 
guided by the following general principles : 

Principles. — 1. The first lessons in fractions should J)'' 
(/iren orally.. No text-l)Ook is needed in teaching the pri- 
mary ideas of the subject. The teacher should drill the 
pupils for several daj-s before taking up the subject in the 
book. 



o68 



:.IETII0I)3 OF TEACHING, 



2. 3Iental and written exercises should he combined in the 
first lessons. The order is, first the idea, then the oral ex- 
pression of it, and then the written exjyression of it. As soon 
as the pupil has an idea of an operation, he should be taught 
to express it in written characters. The seeing of the opera- 
tion will help to make it clear to the understanding and fix 
it in the memory. 

3. The elements of fractions should be taught by means of 
visible objects. The pupil should be led to see the fractional 
idea and relation in the concrete, before he is required to con- 
ceive it abstractl3\ The objects to be employed are apples, 
lines, or circles on the blackboard, etc. An arithmetical 
frame, with long rods cut in sections, is used in the schools 
of Sweden, Prussia, etc. 

4.- The operations in tvritten fractions should be taught to 
young pupils mechanically. They should be drilled upon the 
operations until they are thoroughly familiar with them, even 
before they understand fully the reason for such operations. 
This is in accordance with the principle that, with young pu- 
pils, p)ractice should precede theory. 

5. The Methods or Rules in fractions should be derived by 
analysis and induction. Special problems should be given 
for solution, and the rules or ?>itf//?ofZs of operation be inferred 
from the analysis of these problems. The p7-inciples of frac- 
tions should be first illustrated rather than demonstrated. 
These principles should be committed, and the pupil should 
learn to apply them readily. 

Tilings to be Tanght. — The several things to be taught in 
fractions are as follows : 

1. The idea of each fraction. 

2 The fractional parts of numbers. 

3. Solution of problems requiring the fractional parts of numbers. 

4. The notation of fractions. 

5. Analysis of concrete problems. 

6. The cases of reduction of fractions, and their analysis. 

7. Addition, subtraction, multiplication, and division of fractions. 

8. The rules and the principles. 



TEACHING PRIMARY ARITUMETIC. o()9 

1. Idea of a Fraction. — First, give a lesson on one-half ; 
then on one-third ; then on one-fotxrth^ etc., as far as one-tenth. 
The method is sliown in the foUowing model lesson : 

Model Lesson. — If I divide an apple into two equal parts, what is one 
part called? What are two parts called? How many halves in a whole 
aijle? What is one-half of anything? Ans. One-half of anylhiiuj is 
one of the two equal parts into which it is dioided. 

2. Apply to XiuHfters. — The next step is to apply the 
fractional i>iea to fintling the parts of numbera. This is a 
logical step in advance: the first step was to get a part of a 
unit ; now we pass to finding parts of collections of units. 
To illustrate, suppose we wish to obtain the one-half of 6. 
Show the pupil tliat one of tha two equal parts of 6 is 3, hence 
3 is one half of 6. We then proceed to obtain one-half 
of other numbers, from 2 to 24; then get one-third and. ^i^o- 
thirds of numbers, also one-fourth, two-fourths, etc., of num- 
bers, etc. The next step is to find the fractional parts of 
numbers which do not gioe exact parts ; as ^ of 7, |^ of 11, etc. 

After the pu[)il has the idea, he should he required to give 
a simple solution of the process. Two forms of solution are 
suggested, one resting on multiplication, the other on division. 
The latter will be more convenient in practice, as in finding 
one-half, one-third, etc., of large numbers, we must divide 
them by two, three, etc. The thouglit is, tliat to find one- 
half oi! a number, we divide the number into two equal parts. 

Model Lesson. — Problem. What is one-half of 6? Solution. One- 
half of 6 is 3, because 2 times three are 6. Sol. 2d. One-half of 6 is 
3, because 6 dioided by 2 is 3. Illustration. 6=3 -f-3; hence 3 is one of 
the two equal parts of 0, and 3 is therefore one-half of G. We should also 
get two, three, etc., fractional parts of numbers. Puob. What are two- 
thirds of 6? Sol. One-third of 6 is 2, and two-thirds of 6 are two limes 
2, which are 4; therefore, two-thirds of 6 are 4. Prob. What is J of 7 ? 
Sol. 7 equals 6-fl ; i of 6 is 3, ^ of 1 is ^, etc. 

3. Concrete Problems. — The next step is to appl}^ tliese 

fractions to concrete problems. Thus, " If A has 6 apples 

and B has one-half as many, how many apples has B?" The 

pupil should be required to give a clear and simple solution. 

16* 



370 METHODS OF TEACMIINQ. 

lU'istrrttlon. — Pkob. If A lias apples and B has one-lialf as many, 
how many apples has B ! ■ Solution. If A lias 6 apples and B has one- 
half as many, B has one-half of (J apples, or 3 apples. Prob. If I have 9 
marbles and give "2 thirds of Ihem away, how many will I give away? 
Solution. If I have 9 marbles and give 2 thirds of them away, I give 
away 3 thirds of 9 marbles; one third of 9 marbles is 3 marbles, and 3 
thirds are 3 times ?> marbles, or 6 marbles. 

4. The Notation. — The next, step is to present the notation 
of fractions. This, in practice, may be done in connection 
with some of the previous exercises. The notation may be 
presented in two ways. The teacher njay simply state the 
method of writing the numerator and denominator, and drill 
tiie pupils in writing ui^til they can read and write fractions 
readily. By this method pupils will see no reason for the 
method, and, indeed, will not think to inquire after any reason. 
It will be purely arbitrary and conventional to them. 

Another method is to lead the pupil gradually to the nota- 
tion, somewhat as we ma}' suppose it was reached historical!}'. 
Thus, we may write some fraction, as B-fourths, then abbre- 
viate it to 3-4ths, then still further abbreviate by omitting the 
iA.s, giving 3-4; then represent it by separating the Sand 4 
by an oblique line, as ^4 • ^•''^1 then let this line crowd the 4 
down under the 3 and leave f. Or, we might have the 
name written under the numerator, as, —5 — ; then abbreviate 
it into -^-, and then again into f. Let the teacher illustrate. 

5. Analfjf^iff- — The next step is to apply the fractions in 
the analysis of two or three classes of concrete problems, as 
follows: 1. "If 2 apples cost 4 cents, what cost 3 apples?" 
2. " What will 3 yards of ribbon cost, if | of a yard cost 8 
cents?" 3. "Six is | of what number?" etc. 

lll>tstr'ntion.—\. Prob. If 3 apples cost 4 cents, what cost 3 apples? 
Sol If 3 apples cost 4 cents, 1 apple costs i of 4 cents, which is 3 cents, 
and 3 apples cost 3 times 3 cents, which are 6 cents. 2. Prob. AVliat 
will 3 yards of ribbon cost, if f of a yard cost 8 cents? Sol. If I of a 
yard cost 8 cents, ^ of a j'ard costs .V of 8 cents, or 4 cents, and i!, or 1 
yard, costs 3 times 4 cents, or 12 cents; and if 1 yard costs 13 cents, 3 



TEACHING PRIMAKY ARITHMETIC. 



371 



yards cost Stimos 12 cents, or ;"G cents. 3. Pkob. Six is ? of wliivt num- 
ber? Sol. IfU is ^ of some nuniber, J of the number is h of 6, or 3, and 
|, or the number, is 3 times 3, or 9. 

6. Itedaction of Fractions. — The next step is to present 
some of the simpler cases in the reduction of fractions. Tiie 
several cases of Ivjcliiction are: 1. A number to a fraction; 
2. A fraction to a nunil)er; 3. To higher terms; 4. To lower 
terms; 5. Compound fractions to simi)le; G. To common 
denominator. We should present these cas.es first convrelelt/ 
by iUudration^ aud then recpiire the i)upils to give a sinqjle 
solution of the problems, ^Ve shall illustrate with a few of 
the simpler cases. 

llliistrittioii. — Take the problem, "How many sixths in 5 ?" We may 
illustrate tliis by circles or ll/ies on the board. 
In the first circle, we have three equal parts, 
and two of them are two-thirds. Dividing 
thiiini thirds inlo tw.-) eqiud parts, we see that 
we have sic equal parts, and each part is one- 
sixth ; and we see tluit tlie tw:>-thirds contain 
four sixths; hence, W(! see tliat | equal ^. 
The sune tiling is .shown with the two lines, in wliich the distance be- 
tween tlie two parallc;! horizontal lines indicates the unit. By reversing 
this, we may illustrate liow to reduce //'om higher to lower terms. 

By a similar illustration we can show how to reduce a compound frac- 
tion to a simple one. To illustrate, take the problem, " What is i of ^? " 
Divide the circle into /our equal parts; each part is one-fourth. To ob- 
tain i of ojicfourth, we must divide each 
fourth into two equal parts. Doing this, we 
find we have eicjlit parts in the circle; hence 
each part isone-eijhth; hence one-half oi one- 
fourth is one-evjkth. The line may also be 
used; the line in the margin illustrates finding one-half 0^ one-third. The 
teacher should make constant use of these illustrations, aud require the 
pui)ils also to illustrate the problems. 

7. Aiiolysis in Fractions. — The pupils should learn the 
anali/ses of these cases of fractions. These analyses should be 
simple and concise. The}' are designed to state the steps of 
the judgment in obtaining the results required. In these an- 




/^ 


-"^ 


/ \^ 


y \ 


/ ^ 


/ 


1 / 













372 METHODS OF TEACHING, 

alyses, the unit is made the basis of reasoning; it is a centre 
around which the reasoning revolves. We present tlie analy- 
sis of a few of the cases. 

Cask I. is to reduce a number to a fraction. Prob. How many fourths 
in 3|? Sol. In one there are 4 fourths, and in 2 there are 2 times | or ^ ; 
and f plus f are J^. Case II. is the reverse of this. Prob. In V- how 
many onesf Sol. In one there are |, hence in ^j^- tliere are as many ones 
as 4 is contained times in 11, which are 2|. Another solution of this 
second case is as follows : In one there are four fourths; hence \ of the 
number of /i9wr^/t» equals the number of o?zes; i of 11 equals 2 1. The 
first of these is much more easily understood by children. 

Case III. is to reduce to higher terms. Prob. In f how many sixths? 
Sol. In one there are f , and in \ there are \ of I, or |, and in | there are 
2 times f, or |. Case IV. is the reverse of this, to reduce to lower terms. 
Prob. In | how many thirds? Sol. In one there are f, in one-third 
there are \ of ^, or two-sixths, hence in | tliere are as many thirds as | 
are contained times in |, or |. This case also leads to tlie reducing to a 
common denominator, in which the analysis is like thatjust given. 

Case V. is the reducing a compound fraction, to a simple one. Prob. 
What is }y of I ? Sol. One-third is one of the three equal parts into which 
a unit is divided; if each third is divided into two equal parts, three thirds, 
or the unit, will be divided into three times two, or siz equal parts, and 
each part will be one-sixth of a unit; hence | of | is ^. Another 
Solution. One-third equals |, and ^ of f is ^; hence | of ^ is ^. 

The first solution is a little difficult for a beginner; but it involves 
precisely the mental process of obtaining i of }, and is the one which 
should be used when a child is ready for an analysis; The second solu- 
tion does not show why ^ of i is I, though it obtains the result. It may 
be used with the beginner, but it should be afterward followed by the 
other solution. A celebrated author of Mental Arithmetic gave the fol- 
lowing solution : "One-half of one is h, and if I of one is \, | of ^ is | of 
i, which is ^." The error in this logic is that to explain what is "h 
of ^," the author assumes he knows what "|- of V' is, the more difficult 
thing of the two. 

8. Tlie Other Cases. — All the other cases of Fractions, — 
Addition, Subtraction, Multiplication, Division, and Relation 
of Fractions, — should be solved by analysis, as the pupils 
become able to understand them. The student-teacher should 
be required to show how to give the instruction. Illustrate 
both the inductive and deductive methods. 



TEACHING PRIMARY ARITHMETIC. 373 

9. The Rules. — The pupil needs to be able to derive results 
without going through the analysis each time, and for this 
purpose Rules should be drawn from these anal_yses. These 
may be derived by inference or induction. Thus, in reduc- 
ing 2f to fourths, since in the analysis we take the product 
of 4 and 2 and add the 3, for the number of fourths, we may 
infer the rule, "To reduce a mixed number to a fraction, we 
multiply the integer by the denominator of the fraction, and 
add the numerator to the result," etc. The other rules of 
fractions may be derived in the same way. Another method 
is to derive them from the py^inciples of fractious. The in- 
ductive method is easier for learners, and is preferred in 
primary arithmetic. With beginners, however, it may be well 
to teach the method of doing the work, without giving any 
reason for it; and subsequently-, when they are familiar with 
the rules, they may learn to derive them. Let the student- 
teacher give examples of each case of fractions, and show 
how to analyze and to derive the rules. 

10. The Principles.^ Aher pupils are somewhat familiar 
with these fundamental ideas and processes, they should be 
taught the principles of fractions. These principles may be 
illustrated so that the pupils may have a general idea of the 
manner in which they are derived, or pupils may be required 
to commit and apphj them without any idea of how they are 
derived. A simple solution like the following may be given: 
"Multiply the denominator of | by 2." Sol. — If we multiply 
the denominator of | by 2, we have 3 eighths, which is one- 
half as ranch as S fourths, since eighths are onl}^ half as great 
as fourths; from which we infer that muUiphjing the denom- 
inator by 2 divides the fraction by 2. When the pupil is 
ready to understand the demonstration of the principles, a 
real demonstration should be given, and not some loose, in- 
definite statement, such as we find usually presented. For 
the more general demonstration, see the Treatment of 
Fractions in arithmetics. 



874 METHODS OF TEACHING. 

The stuflent-teacher should now be required to outline the 
course of instruction in Fractions in primary arithmetic, and 
show by model lessons how he would teach them. 

V. Teaching Denominate Numbers. 

Principles of Insfrnctioii. — In giving instruction in De- 
nominate Numbers, teachers should be governed by the fol- 
lowing principles: 

1. Denominate Numbers should be taught concretely. The 
teacher should have the actual measures to illustrate the sub- 
ject. If they are not in the school-room, the teacher can pro- 
cure them at a trifling nxpeiise. In some text-books on pri- 
mary arithmetic, we find pictures of the measures; but the 
measures themselves are worth much more than the pictures 
of them. In fact the pictures give an inadequate idea of the 
measures, and often an incorrect one. The neglect of this 
principle is very common. Most teachers have the pupils re- 
peat the tables without any illustration of their meaning,' 
The result is, that these "weights and measures" are to many 
pupils merely so many words without an^?^ corresponding 
definite ideas. 

2. The teacher should require the pupils to make a practi- 
cal application of these measures. He should drill them on 
measuring and judging of the length of rooms, the height of 
ceilings, the area of surfaces, the volumes of solids or vessels, 
the amount of land in fields, the amount of plastering in a 
room, the amount of carpet required to cover a floor, etc., etc. 
These measures will thus become actual and practical realities, 
and not mereh^ a lot of names to be committed to raemor3'. 

Measures of 3Ioney. — In teaching the measures of Money, 
the teacher should show the pupils the cent^ dime, dollar, 
eagle, etc. Ever^^ school should bej^rovided with a collection 
of coins to illustrate the subject. There should be specimens 
also of the English penny, half-penny, the shilling, sixpence, 
florin, etc. In teaching French money, there should be 



TEACHING PRIMARY ARITIIMETTC. 375 

specimens of the franc ^ half-franc^ five centimes or sou. ten 
centimes or two sous. lu teaching German money we shonld 
present to the pnpil the mark, tlie thaler, the groschen, etc. 
The tables are also to be committed, written on the board, 
and repeated. 

Pleasures of Weight — In teaching the table of Weights, 
the pupils should be shown the different weights, — the ounce, 
tlie pound, etc., — and be required to examine and handle them 
until they are entirely familiar with them. They should see 
and handle the pennyweight, the ounce, the pound, Troy; 
also the scruple, dram, ounce, and pound. Apothecaries. 
Tliere should be a pair of scales in the school-room to weigh 
objects. Pupils should also be required to " heft" different 
objects, as a book, a chair, etc., to learn to judge of the 
weight of objects. The tables of weight should be studied 
and committed. We should also have specimens of the 
gram, decagram, and kilogram. 

Measures of Lcnf/th. — The teacher should give the pupil 
definite ideas of all the measures of length. There should be 
theybo^ and yard rules, divided into inches, half-inches, etc.. 
Have the length of a rod marked on the wall or floor, show 
the pupils the distance of a mile, a half-mile, etc. Have a 
meter properly divided, show its relation to the yard, and 
give definite ideas of the decimeter, centimeter, etc. Pupils 
should also be drilled in estimating the length of objects, dis- 
tances, heights of ceilings, of trees, etc. 

3[easures of Surface. — The teacher should mark on the 
board a square inch, square foot, and square yard, to show 
what is meant by these surfiices, and also to give definite 
ideas of them. Show also the reason why 9 sq. ft. njake one 
square yard, and 144 sq. in. equal a square foot. Measure ol 
a square rod out in the field, and also an acre, and have pupils 
judge of the number of acres in a field. Have pupils remem- 
ber that a square about 209 feet, or 70 paces on a side, is an 
acre. Teach the surfaces in the metric system in the same 



37() METHODS OF TEACHING. 

way. Have the pupils study and recite the table of square 
measure. 

3Tensures of Volume. — The teacher should show the pupils 
a cubic inch and a cubic foot. He should draw them and. also 
the cubic \jard upon the blackboard. He should also, as 
clearly as possible, show the relation of them, — that is, that 
27 cu. ft. equal a cubic yard, and 1728 cu. in, make a cubic 
foot — by a figure on the board, or by blocks prepared for 
the purpose. Give them an idea of a co7'd by takiug a lot 
of little sticks 4 inches long, and making a pile 8 inches long 
and 4 inches high, and show them that a cord contains 128 
cu. ft. To give them an idea of a coi^d foot, measure off 1 
inch of the little cord, and run a thin stick or a piece of wire 
down, cutting off a part of the pile 1 inch long, which will 
represent a cord foot ; the}' will thus see that 8 co7'd feet 
make a cord. 

Liqnid Measure. — In teaching Liquid Measure, haA^e the 
measures in the school-room, — the gill, the pirti, the quart, 
and the gallon. Show them by actual trial that 4 gills Avill fill 
a pint, 2 pints a quart, etc. Barrels and hogsheads can be 
seen at a store. We should also have samples of the Apothe- 
caries' liquid measures in the school, — the minim, fluidrachms, 
fluidounces, etc. 

Dry Measure. — In teaching Dr}^ Measure, the pint and 
quart at least should be in the school-room. Have the pupils 
call at the grocer's to see the jjeck and bushel, or examine 
these measures at home, if their parents have them. They 
should also be led to compare the liquid quart and dry quart, 
etc. The metric sj'stem of measures should also be in the 
public school, and the pupils be drilled on them. 

Measures of Time. — Time will be quite easil}^ taught, as 
the measures are in such constant use. We should begin 
with the day as the most natural unit, and pass to the other 
measures. We should explain how nature fixes the day, and 
month, and year, and give the meaning of these terms. By 



TEACHING PRIMARY ARITHMETIC. 377 

means of a clock, we can teach the number of hours in a da}', 
the number of minutes in an hour, and of seconds in a minute. 
The number of da3's in each month is best taught by the 
stanza, "Thirty days hath September," etc. This can also be 
remembered b}- the hand, the fingers representing January, 
March, May, etc., and the spaces between them representing 
February, April, June, etc. We should also show them that 
the calendar begins one day later each year, and two days 
later after a leap year, and explain the reason for it. When 
they are prepared to understand it, we can explain the reason 
for leap year, etc. 

Circular Measure. — In teaching Circular Measure, draw 
a circle on the board, and teach the different parts — circum- 
ference, semi-circumference, quadrant, arc, etc. Then explain 
the division into 360 equal parts, each called a degree; that 
the semi-circumference contains 380°, and the quadrant 90°. 
Then show that the degrees are divided into 60 equal parts 
called minutes^ and the minutes into GO equal parts called 
seconds. Show that all these a.i'e parts of the circumference, 
that tho}^ are not of a fixed length, but differ in size with 
different circles. Call attention also to the difference between 
minutes and seconds of circular measure and of time measure. 

A drill like this in Denominate Numbers will give the 
pupils definite ideas of what the}'^ are committing, and will 
make these tables a reality to them, and not a mere collection 
of abstract names. It will make them interesting to pupils 
and much more easily remembered than when taught in the 
usual abstract method of our schools. When the classes are 
more advanced, the many interesting facts concerning the 
tables — the origin of their names, of their units, etc. — may be 
presented. 



CnAPTER IV. 

TEACHING MENTAL ARITHMETIC. 

AFTER completing the course in Primary Aritlimetic, the 
pupil raa}^ take a complete course of Mental Aritlimetic 
in one book, and a complete course of Written Arithmetic in 
another book; or these two courses may be combined in one 
book, as the teacher prefers. lu this chapter we shall speak 
of the Importance of Mental Arithmetic, its Nature, and the 
Methods of Teaching it. 

I. Importance of Mental Arithmetic. — Mental Arithmetic 
has become one of the most popular studies of the public 
school; in manj'^ places it has been the idol of the school- 
room around which have centered the affections of teachers, 
pupils, and parents. This preference is not a mere whim, but 
is founded on the intrinsic value of the subject, which we 
shall brief!}' consider. The value of Mental Arithmetic is 
two-fold ; first, as a mental discipline, and second, as a means 
of cultivating arithmetical power. 

llenfal Discipline. — The science of numbers before the 
introduction of Mental Arithmetic, was far less useful as an 
educational agency than it should have been. Consisting 
mainly of rules and methods of operations, without leading 
the pupil to see the reasons for these operations, it failed to 
give that high degree of mental discipline which, when prop- 
erly taught, it is so well adapted to afford. By the introduc- 
tion of Mental Arithmetic a great change has been wrought 
in this respect; the spirit of analysis has entered into the 
science; and now the science of numbers presents one of the 
lest, if not the very best, means of discipline in the curricu- 
lum of tlie common school. 

1. Mental Arithmetic gives culture to the reasoning facul- 
(378) 



Tli ACHING MENTAL ARITHMETIC. S79 

ties. No stud}' in the school equals, suvel3'' none surpasses, 
Mental Arithmetic in giving exercise and development to the 
power of reasoning. It is a system of practical logic ; all its 
processes are in accordance with the laws of thought; every 
step is a judgment direct or indirect; and the entire subject 
is permeated with the principles of logic. Its processes are 
analytic, and it thus trains the mind to the most rigid and 
severe analysis. Every truth is bound to ever}' other truth 
by the thread of related thought; and the mind of the pupil 
becomes habituated to following a chain of logically connected 
judgments, until it reaches a desired conclusion. It is thus 
clear that Mental Arithmetic must be very valuable in giving 
culture to the power of thonu'lit. 

2. DIental Arithmetic cultivates the poicer of attention. 
When properly taught, no stud}' compares with Mental 
Arithmetic in this respect. Tht. problem, as read by the 
teacher, must be repeated by the pupil, each number is to be 
remembered in its pro[)er place, and each condition properly 
related ; and this can be done only b}' the most careful atten- 
tion. Pu[)ils trained in this way acquire the abilitj' to repeat 
long and complicated problems with ease and accuracy. Such 
disci|)line enables them to fix their minds upon a discourse 
and reproduce much of what they hear. 

3. ^rental A rithmetic gives culture to the memory. Memory 
depen Is upon the power of attention: we remember that 
which we fix in the mind by close attention; we forget that 
to wliich we are inattentive. Few persons, after hearing a 
sermon or discourse, can tell you anything definite concerning 
it, because tlicy are careless and inattentive listeners. Any- 
thing that trains the mind to liabits of close attention tends 
to give strength and reliability to tiie memory. Mental 
Ai'ithmetic, therefore, in its disci[)line of the attention, is an 
ini[)ortant means of training the memory to habits of readi- 
ness and accurac}-. 

4. 3Iental Arithmetic cultivates exactness of language. It 



380 . _ METHODS OF TEACHING. 

is so rigidly exact in its processes of thought that it requires 
corresponding exactness in its language. The right word 
must be used in the right place, or the reasoning will be at 
fault. The language of Mental Arithmetic is simple, clear, 
and precise; and the mind, becoming habituated to such forms 
of expression, will naturally incline to use them in the con- 
sideration of subjects not mathematical. 

5. Mental Arithmetic sharpens and atrengthens the mind 
in general. The sj'Stem of rigid analysis gives point and 
penetrating power to the mind, and enables a person to pierce 
a subject to its core and discern its elements. In this respect, 
Mental Arithmetic is a sort of mental whetstone which gives 
edge and keenness to the mind. Old Robert Recorde called 
his work on arithmetic the "Whetstone of Witte;" had he lived 
until the era of Mental Arithmetic, he would have seen the 
full meaning of his words, for mental arithmetic is indeed a 
whetstone of wit, a sharpener of the mental faculties. 

It also strengthens the mind as well as sharpens it. The 
mind, like a muscle, grows tough by hard work; we toil for 
strength in studj^, as we do upon the playground or in the 
gj'^mnasium. Mental Arithmetic is a mei>tal gymnastics; 
through it the mind grows strong and tough, taking hold of 
difficulties with a will, laughing at obstacles, and rejoicing in 
the investigation of the ii^tricate and profound. 

6. Mental Arithmetic prepares a pupil for extemporaneous 
speaking. In solving a problem the pupil must stand up be- 
fore his class, hold the conditions of his problem clearly in his 
mind, and proceed to develop the matter under consideration 
in logical forms of thought and expression. This is precisely 
the discipline needed to make a good extempore speaker. It 
also tends to correct the habit which many speakers have of 
talking without saying much. The good speaker is one who 
utters thought, and not words merely ; and the study of men- 
tal arithmetic tends to cultivate speakers who think and utter 
thou2,ht. 



I 



TEACHING MEXTAL AUITHMETIC. S8l 

Arithmetical Power. — The influence of Mental Arithmetic 
has been no less mai'ked upon the science of arithmetic itself. 
Consisting heretofore of mechanical methods for finding re- 
sults, it was dry, uninteresting, and difficult. Few pupils 
attained any excellence in it ; and many acquired a positive 
distaste for the subject. But these things have passed away; 
a new era has dawned upon the science of numbers ; a " royal 
road" to arithmetic has been found ; and it has been so 
graded and strewn with the flowei's of reason and philosophy 
that it is now full of interest and pleasure to the youthful 
learner. The agent tliat has produced this change is the 
method of analysis which we know as Mental Arithmetic. 

1. The study of Mental Arithmetic gives the pupil the power 
of independent thought in arithmetic. The spirit of mental 
arithmetic is analysis. It is not merely oral arithmetic ; it is 
analytical arithmetic ; and in this consists its power. By it 
pupils become able to investigate for themselves, and are no 
longer bound down to the dictation of rules. " The rule says 
so," is no longer the touchstone of the science or the key to 
the result ; but a careful comparison of the conditions of the 
problem will enable the pupil to make his own method and 
derive his own ru^e. By it lie becomes, not a mere arithmet- 
ical machine, hnt an original thinlier, understanding what he 
does, and prepared to make new investigations and new dis- 
coveries in the science. If we wefe obliged to choose be- 
tween a course in mental and one in written arithmetic, we 
should take a complete course in mental in connection with 
the fundamental rules of written arithmetic ; and we would 
turn out better-trained thinkers in arithmetic than if we had 
drilled them in the usual course of written arithmetic. 

2. The study of Mental Arithmetic is an excellent prepara- 
tion for Algebra. Arithmetic and Algebra are intimately 
related, algebra being a kind of general or S3'mbolic arithme- 
tic. The anal3-sis of mental arithmetic is especially similar 
to the elementary reasoning of algebra, the main difference be- 



382 METHODS OF TEACHINQ, 

ing: that the latter employs s^ymbols which render it more 
concise and general. The one insensibly glides into tlie otlier 
by the substitution of a symbjl for a word; and it is tlms 
evident that the stud}^ of m3ntal arithmetic is a most valualde 
preparation for the study of algebra. 

Its Great lvalue. — No words can convey a full appreciation 
of the importance of mental aritlimetic. Only tliose who 
experienced the transition from tlie old methods to the new, 
can full}" realize the supreme value of the study. Indeed, 
we believe that the method of mental arithmetic is the great- 
est improvement in modern education; and the world owes 
a debt Qf gratitude to Warren Colburn, its author, which it 
can never ]}t\.y. Though there has been a recent reaction in 
public sentiment against the subject, we believe that it is 
merely a wave of opinion and cannot be permanent. Mental 
arithmetic is the great source of discipline to the power of 
thought in our public schools. When properly taught, it 
gives quickness of perception, keenness of insight, tougliness 
of mental fibre, and an intellectual power and grasp that 
can be acquired by no other primary study. To omit, there- 
fore, a thorough course in mental arithmetic in tlie com- 
mon schools, is to deprive the pupils of one of the principal 
sources of thought power. 

II. Nature of Mental ARiTri>rETic. — In order to teach 
Mental Arithmetic properly, or to appreciate its value as an 
educational agency, its nature should be clearly understood. 
It is a popular view that mental arithmetic is merely the 
working of problems in tlie mind, and this is the opinion of 
many who oppose it as a distinct stud}-; but this is a mistake, 
and one that should be corrected. The genius of mental 
arithmetic is not nierel}^ the " working of problems in the 
head," but the analytic and inductive treatment of the science 
of numbers. We shall attempt in a few words to explain its 
nature. 

General Nature. — A system of Mental Arithmetic is de- 



TEACHING MENTAL ARITHMETIC. 883 

veloped upon the principles of Analysis and Induction. The 
reasoning processes are purely analytical, not demonstrative ; 
and tlie methods of operation should be derived from tiiese 
analyses by Inference or induction. Each problem is resolved 
into its simple elements, and the relation of the elements, lead- 
ing to the desired result, determined by comparison. When 
we wish to derive rules to apply to other problems of the same 
class, Ave notice the process generated by the anal3'sis, and 
generalize this process into a rule. 

This brief statement shows the philosophy upon which a 
S3^stem of mental arithmetic is founded. It is purely analj-tic 
and inductive ; and not synthetic and deductive, like written 
arithmetic. Analj'sis determines the process in any particu- 
lar case, and Induction derives the method that applies to all 
problems of the same class. Anal3-sis and Induction are 
the golden keys which unlock the various complex com- 
binations of numbers ; they are the magic wands whose 
touch unfolds the mysterious and beautiful combinations of 
numbers. 

Analysis. — Arithmetical analysis assumes the Unit to be 
the fundamental idea of arithmetic, and comprehends all num- 
bers and their relations through their relation to the unit. It 
compai'cs numbers and the effects produced by a number of 
equal causes through their relation to the unit or the effect 
of a single cause. It comprehends a fraction by a clear 
apprehension of the relation of the fractional unit to the inte- 
gral unit ; and thus develops the principles and methods of 
fractions. In this manner the whole science is evolved, pre- 
senting one of the most beautiful examples of pure logic that 
can be found in any science. 

The simplicity and beauty of this process is seen in the fact 
that the unit is the fundamental idea of arithmetic. Arith- 
metic begins with the unit ; all numbers arise from a repeti- 
tion of the unit ; fractions have tlieir origin in the division of 
the unit. Hence, in the comparison of numbers the unit nat- 



384 ■ METHODS OF TEACHING 



^ 



urally becomes the basis of the reasoning process. We reason 
to the unit, from the unit, and through the unit. The unit is 
the foundation upon which we build ; it is the stepping-stone 
in the transition of thought ; it is the centre around which the 
process of reasoning revolves. In it we have an illustration 
of the general principle that the One lies at the basis of all 
things. All science is a striving after the One which con- 
tains the All; the Cause which contains the phenomena, the 
Law which contains the facts, the one principle that binds all 
variety into unity. 

Coutparing Integers — In applying this analysis to num- 
bers, we have three cases: First, where we pass from the 
unit to a number ; second, where we pass from a number to 
the unit; and third, where we pass from a number to a number. 
In the first and second cases, the transition is immediately 
made, since the relation is immediately apprehended, being 
given in the genesis of numbers. In the other case, the com- 
parison is not immediately seen ; it must therefore be made 
by the intermediate comparison of each to the unit. That is, 
in passing from a collection to a collection, or from one num- 
ber to another, we first pass to the unit and theny/-o??i the 
unit. 

Thus, take the problem, "If 4 apples cost 12 cents, what 
will 5 apples cost?" Here the cost of Jf. aiyples is the known 
quantity, the cost of 5 apples is the unknown quantity ; the 
object is to determine the unknown by comparing it with the 
known. This comparison cannot be made immediately, since 
the mind does not readily perceive the relation between five 
and /our; we therefore pass from /our to o?ie, and then from 
one to five. Thus the analysis is: " If /bz/r apples cost 12 
cents, one apple costs ^ of 12 cents, or 3 cents; and if one 
apple costs 3 cents, /ue apples cost 5 times 3 cents, or 15 
cents." This problem also illustrates the first and second 
cases of comparison. 

Com^pnring Fractions. — With Fractions the same law 



TEACHING MENTAL ARITHMETIC. 385 

holds as with Integers, though the existence of two units^ 
the integral unit and the fractional unit, somewhat compli- 
cates the process. There are three distinct cases as in 
integers: (1) passing from an integer to a fraction; (2) passing 
from a fraction to an integer ; (3) from a fraction to a frac- 
tion. In tlie first case, we pass to the unit, then to the 
fractional unit, and then to the collection of fractional units. 
In the second case we pass to the. fractional unit, then to the 
integral unit, and then to t\i(i collection of integral units. In 
the third case we pass to the fractional unit, then to the 
integral unit, then to the other fractional unit, then to the 
collection of fractional units. 

We give a problem of the third class, which includes also 
what in both of the others differs from the case of integers. 
Take the problem, "If | of a j^ard of cloth cost 8 cents, 
what will I of a yard cost?" The solution is as follows: " If 
2 thirds of a yard cost 8 cents, one-third of a yard costs ^ of 
8 cents or 4 cents, and three-thirds, or one yard, cost 3 times 
4 cents, or 12 cents; if one yard cost 12 cents, one-fourth of 
a yard cost ^ of 12 cents, or 3 cents, and three-fourths of a 
yard cost 3 times 3 cents, or 9 cents." 

Here the object is to compare | with f , which we do by the 
intermediate relations of the units. It 
is as if one stood at A and wished to j^ 

pass to E. The mind cannot step di- ^rL, jJ L. [-Ha/ 
rectly over from A to E, so it first -b ^t^ — 1 

steps two steps down to B, then three 

steps up to C, then four steps down to D, then three steps up 
to E. 

Application of Analysis. — These anal^'ses represent the 
spirit of Mental Arithmetic. Such processes of reasoning run 
through the entire science. Tlie subject of Fractions, present- 
ing many interesting cases, is beautifully \ni folded by it. It 
can also be applied to problems in Simple and Compound 
Proportion, Partitive Proportion, Medial Proportion, etc., 
17 



886 METHODS OF TEACHING. 

giving simple and elegant solutions. The subject of Percent- 
age and Interest is also developed by anal3'sis with great 
simplicity and elegance. 

Induction — The office of Induction in Mental Aritlimetic 
is to derive methods of operations or rules from the analyses. 
The object of these methods is to enable us to reach the result 
directly by a mechanical operation, instead of going through 
tlie process of anal3'sis ever}' time we need a result. Thus, 
suppose we wish to find a method of reducing fractions to 
lower terms; by analysis we reduce some fraction to lower 
terms, as -^j equals f ; and then, by examining the process or 
by comparing the two fractions, we can derive the rule for 
reducing a fraction to lower terms. The same thing can be 
done for all the many cases which arise in fractions. 

Such inferences are necessary in Mental Arithmetic if we 
would attain any methods of operation, independent of the 
analyses. In Written Arithmetic these rules ma}' be derived 
b}^ demonstration ; but no demonstration is appropriate to the 
spirit of Mental Arithmetic. To introduce demonstration 
in Mental Arithmetic would destroy or mar its anah'tic 
s))irit, which is the distinctive characteristic of the branch. 
By the use of induction, the analytical spirit of the science is 
preserved, while it becomes practical in its methods and con- 
cise in its operations. 

III. Methods of Teaching Mental Arithmetic. — The 
course in Mental Arithmetic is so definitely laid down in our 
text-books, and the methods of instruction so clearl}' indicated, 
that but little need be said with respect to methods of teach- 
ing the subject. Onl}'^ a few suggestions will be presented. 

Pupils' Preparnfion. — Pupils in preparing their lessons 
should be careful to go through the form of analysis, making 
the clear expression -of the reasoning the test of their knowl- 
edge of the lesson. To perform the mechanical oi)erations 
necessary to attain the results is not sufficient. They may 
aid themselves, however, with pencil by writing out the solu- 



TEACHING MENTAL ARITHMETIC. 387 

tion, where it is long and complicated. The reducing of tho 
solution to writing requires exactness of thought, and the 
seeing of the analysis will aid in fixing it in the under- 
standing. 

Pupils should be especially careful to depend upon them- 
selves in solving the problems. The habit of a few pupils in 
the class working out the more difficult problems for the 
others, deprives the pupils assisted of the principal benefit of 
the stud}-. A pupil should never be allowed to take the solu- 
tion of another pupil or of the teacher and commit it to 
memory. It is better not to know how to solve a problem than 
to solve it with the memor}'. 

The Recitation. — At the recitation, the teacher should 
read the problem and require the pupil to arise, repeat it, and 
give the solution. The pupil should not be allowed to use 
the book during recitation. The practice of some teachers of 
allowing the pui)ils to read the problems and solve them from 
the book is a needless and a pernicious one. The book is not 
needed in recitation by the pupils ; a ver}' little practice will 
enable them to reproduce long problems and hold the condi- 
tions in the mind with entire ease. More than half the benefit 
of the study is lost when the pupils solve with the book in 
their hands. 

Pupils ma}' be required to write out their solutions on paper 
or on the blackboard. This is especially convenient when 
the class is large, some being busy writing out the solutions, 
while others are reciting orally. The solutions as written 
should be not merely the operations, as in written arithmetic, 
but a complete analysis of the problem. Where the solution 
makes equational thought prominent, the form of writing may 
approximate that used in algebra. 

Great care should be taken that the language of the solu- 
tion be concise and accurate. The pupil should be required 
to say just what he means. The teacher should not accept 
his " O, that's what I meant," when he said something quite 



388 METHODS OF TEACHING. 

different. The singular and plural should be used as accu- 
rately as they can be in the language of arithmetic. We 
should insist also upon a uniformity of tenses in a solution, 
for pupils incline to get their tenses very much mixed in 
their forms of statement. 

Blethods of Recitation. — There are several different meth- 
ods of recitation in mental arithmetic, which we shall name 
and describe. Some of these are preferred to others, but all 
may be used occasionally with advantage. 

Common Method. — By tliis method the problems are 
assigned promiscuously, the pupils not being permitted to 
use the book during recitation, nor retain the conditions of 
the problems by means of pencil and paper, as is sometimes 
done. The pupil selected by the teacher arises, repeats the 
problem, and gives the solution, at the close of which the mis- 
takes that may have been made should be corrected by the 
class and the teacher. 

Silent Method. — By this method the teacher reads a prob- 
lem to the class, and theu the pupils silently solve it, indicating 
the completion of the solution by the upraised hand. After 
the whole class, or nearly the whole class, have finished the 
solution, the teacher calls upon some member, who arises, re- 
peats the problem, and gives the solution, as in the former 
method. 

In this method the whole class solves every problem, thus 
securing more discipline than by the preceding method. It, 
however, requires more time than the former method ; hence, 
not so many problems can be solved at a recitation. Wc 
prefer the first method for advanced pupils, and the second, 
at least a portion of the time, with j^ounger pupilsi It may 
also be used now and then for variety. 

Chance Assignment. — This method differs from the first 
only in the assignment of the problems. The teacher marks 
the number of the lesson and tlie number of the problem upon 
small pieces of paper, which the pupils take out of a box passed 



TEACHING MENTAL ARITHMETIC. 389 

around by the teacher or some member of the class. The 
teacher, then, after reading a problem, instead of calling upon 
a pnpil, merely gives the number of the problem, the person 
having the number, arising, repeating, and solving it. By 
this method the teacher is relieved of all responsibility with 
reference to the hard and easy problems ; and it is also be- 
lieved that better attention is secured with it. It is particu- 
larly adapted to reviews and public examinations. 

Double Assignment. — By this method the pupil who receives 
the problem from the teacher arises, repeats it, and then as- 
signs it to some other pupil to solve. It may be combined 
with either the tirst or second methods. The objects of this 
method are variety and interest. 

Method by Parts. — By this method, different parts of the 
same problem are solved by different pupils. The teacher 
reads the problem and assigns it to a pupil ; and after he has 
given a portion of the solution, another is called upon, who 
takes up the solution at the point where the first stops ; the 
second is succeeded in like manner by a third ; and so on 
until the solution is completed. The object of this method is 
to secure the attention of the whole class, which it does very 
effectually. It is particularly suited to a large class consist- 
ing of young pupils. 

Unnamed Method. — By this method the teacher reads and 
assigns several problems to different members of the class be- 
fore requiring any solutions, after which those who have re- 
ceived problems are called upon in the order of assignment 
for their solutions. There are several advantages of this 
method. First, the pupil having sometime to think of the 
problem, is enabled to give the solution with more promptness 
and accuracy ; and, second, the necessity of retaining the 
numbers and their relations in the mind for several minutes 
affords a good discipline to the memory-. 

In regard to these methods, the first, second, and third are 
probably the best for the usual recitations ; but the other 



390 METHODS OF TEACHING. 

methods can be emplo^^ed very profitably with younger classes, 
or, in fact, with any class, to relieve monotony and awaken 
interest. With advanced pufjils we prefer the first method, 
or the first combined with tiie third. 

Errofsto be Avoided. — There is a large number of errors 
to which pupils in every section of the country are liable, a 
few of which we shall mention. There are many words which 
pupils in their haste mispronounce, and also many com- 
binations, which by a careless enunciation make ridiculous 
sense, or nonsense. We call the attention to a few of them, 
suggesting to the teacher to correct these and others he 
may notice. 

''ylmZ" is often called " an;" "/or" is called "/«r,-" "o/" is 
pronounced as if the o was omitted ; words commencing witli 
wh, as when, which, where, etc., are pronounced as if spelled 
''loen," "w/>7)," "iof??-e," etc. '■'■Gave, him^^ is called '■'■gavim ;'" 
''did /i.e" is c;dled ''diddij;'' ''had /«?" is called "haddy;'' "pioe 
him^^ is called "givim;^^ "give her'''' is called "giver ;'" "which 
is" is often changed into " witches ;^' and "how many'' is fre- 
quently transformed into " hominy." " How many did each 
earn" is often rendered " hominy did e churn." 

A very common error, and one exceedingly ditricult to cor- 
rect, is the improper use of the and are ; as in tlie following 
solution : "If 2 apples cost 6. cents, one apple will cost the h 
of 6 cents, which are 3 cents." Here "the" is superfluous, and 
" are" is ungrammatical. Pupils are so determined upon the 
use of '*the" that we suggest the placing of a " big the" upon 
the board, and allowing the class to point to it every time the 
mistake occurs. 

The following is a frequent error : "If one apple cof^t 3 cents, 
for 12 cents you can buy as many apples as 3 is contained in 
12, which are 4 times." The objections are, first, 3 is not con- 
tained any apples in 12 ; secondly, the result obtained \s times, 
when it should be apples, or a number which applies to both 
times and apples. The solution siiould be, "You, can buy as 



TEACHING MENTAL ARITHMETIC. 391 

many apples for 12 centa as 3 is contained times in 12, which 
are 4." 

With regard to is and are, it is not easy to determine which 
should be used in some cases in Arithmetic. It may be that 
it would be better to use the singular form always, whether 
the subject is an abstract or a concrete number ; thus, 8 is 2 
times 4, and 8 apples is 2 times 4 apples. But since custom 
sanctions the use of" are" with a concrete number as a sub- 
ject, it is necessary to adhere to that form. There is some 
authority for using " is" in the " Multiplication Table," and 
it would be at least conA^enient if the singular form were uni- 
versally adopted. 

Pupils have some difficulty in knowing how to read such 
expressions as $|. They object to saying " | dollars,^' since 
there are not enough to make dollars, and they also object to 
saying "| of a dollar, ^[ since there are only 3 thirds in a 
dollar. The second is undoubtedly a correct reading, remem- 
bering that I is an imjyrojjer fraction. 

The following error is almost universal : " 2| apples" is read 
•' 2 and 3 fourth apples,^^ instead of " 2 and Z fourths apples.'^ 
The expression " f times^^ is sanctioned by custom, although 
it is not strictly in accordance with grammatical principles. 
It is rather more convenient than the expre^^sion f of a time, 
although evidently a violation of the rules of language 

Coitcliision The student teachers will now present a com- 
plete outline of the subject of Mental Arithmetic under the 
several heads: 1. Fundamental Rules; 2. Introduction to 
Fractions ; 3. Treatment of Fractions ; 4. Denominate Num- 
bers ; 5. Proportion ; 6. Percentage and Interest ; Y. Problems 
for Analysis. They should be able to state the different cases 
which arise, give a problem illustrating each case, and present 
a model solution. Let the teacher ever bear in mind that in 
teaching mental arithmetic, he should aim at the following 
objects: Accuracy of memory, clearness of thought, siinpliC' 
ity of analysis, and conciseness and exactness of expression. 



CHAPTER VL 

TEACHING WRITTEN ARITHMETIC. 

IN connection with the course in Mental Arithmetic, there 
should also be a course in Written Arithmetic. ' This 
course may be combined in the same book, or presented in 
different books, as the teacher prefers. In this chapter we 
shall speak of the Nature of the Course, and the Methods of 
Teaching the subject. 

I. Nature of Written Arithmetic. — Written Arithmetic 
differs from Mental Arithmetic in several respects. The ob- 
ject of Mental Arithmetic is the analysis of numbers ; the 
object of Written Arithmetic is the attainment of skill in cal- 
culation. Written Arithmetic is a calculus, and the primary 
object is to learn to work with the Arabic system. The second 
object is the attainment of practical methods of operation, 
and the acquisition of readiness and accuracy in the use of 
these methods. 

Method of Treatment. — The method of treatment in Writ- 
ten Arithmetic should be more deductive than that of Mental 
Arithmetic. The definitions which in Primary Arithmetic 
and Mental Arithmetic are given in the inductive form, should 
here be presented deductively. In the previous course the 
rules should be derived by induction from the analyses; but 
in Written Arithmetic the deductive method must also be 
employed. Here many things are to be demonstrated, and 
demonstration is a deductive form of reasoning. While 
analysis and induction are often used, 3'et the spirit of the 
science is deductive and demonstrative rather than analytic 
and inductive. 

, Arrangetnent. — The arrangement of the subjects in the 

(392) 



TEACHING WRITTEN ARITHMETIC. 393 

text-book nsed should be both scientific and practical. By a 
scientific ai-rangementis meant such an order as the logical de- 
velopment of the subject suggests. By a practical arrange- 
ment is meant such an order as is best adapted to the wants 
of pupils in pursuing the study. A merely scientific arrange- 
ment, however satisfactory to the accomplished arithmetician, 
would not be sufficiently progressive to meet the purpose of 
instruction. A merely practical adaptation of the easy and 
difficult parts to suit the young learner, might completely 
Ignore the logical relations of the science, and tluis fail to 
give that mental discipline which the logical evolution of truth 
imparts. These two methods sliould run together; the work 
should be practically adapted to instruction, and at the same 
time the i)hil<)so|)liical srnrit of the science should be preserved. 

The Gifiddtioii. — The course in Written Arithmetic 
should 1,-e carefully adapted to the different classes of i)ui)ils 
wlio use it. It should be simple enough for young pupils, and 
yet sufficientl}' advanced for those of more mature minds. 
This adaptation maybe accomplished in two or three diff"erent 
ways. The first part of the work should be very simple, the 
difficulties gradually increasing as the pupil acquires strength 
and culture. Tlie teacher may omit certain subjects with 
elementary classes until review, or until the pupil is pre- 
pared for them. Thus the more difficult matter will be left 
for the pui)il until he shall have become somewhat fLimiliar 
with the easier principles and rules, and shall have gained 
mental strengtli to cope with the greater difficulties. Another 
object gained by this plan, is the interest that new matter 
gives to a review. 

The Reasonhtff In Written Arithmetic, as previously 

stated, the methods of reasoning are more synthetic and de- 
monstrative than in Mental Arithmetic. Thus, many subjects 
which in Mental Arithmetic we treat analytically, in Writ- 
ten Arithmetic we should treat by demonstration; as may be 
Been in Fractions, Percentage, etc. Besides this, there are 
17* 



39 i METHODS OF TEAGHTXG. 

many subjects in Written Arithmetic which are purely deduc- 
tive and demonstrative in their nature; as Proportion, Pro- 
gressions, Evolution, etc. Hence, the pupil will be required 
to learn demonstrative reasoning as well as arithmetical 
analysis. 

The Principles. — Arithmetic as a science involves, and as 
an art is based upon, certain principles ; and the most import- 
ant of these should be distinctly stated and clearly demon- 
strated. The form of statement should be deductive; and, 
when not too dithcult, the method of demonstration should 
be deductive also. In other cases the truth may be shown 
inductively, suggesting to the pupil, however, that it is sus- 
ceptible of rigid deductive demonstration. 

Where the principles are essential to the development of a 
subject, they should be given at the beginning of the treat- 
ment of it ; in other cases, they may be stated at the close of 
the subject. Thus, in Least Common Multiple, Greatest Com- 
mon Divisor, Common Fractions, Proportion, etc., the princi- 
ples are given first, and the development based upon them; in 
the Fundamental Rules, etc., a knowledge of some of the prin- 
ciples not being essential to the development of the subjects 
themselves, may be given after them. 

The importance of principles in written arithmetic should 
not be overlooked. Until within a few j^ears, American text- 
books and American instruction almost completely ignored 
the principles" of the science, making arithmetic to consist 
entirely in the solution of problems. This is a great error, 
and one most pernicious in mental discipline. Especially is 
attention to principles important in Normal instruction, 
where the pupil expects to teach others. No matter how hard 
a problem he can solve, if he cannot give neat and clear expla- 
nations, he is unfit to be an instructor of others. It should be 
remembered also that a clear knowledge of the principle makes 
a problem, otherwise diflficult, comparativeh^ easy. 

The Problems. — Problems are of two kinds, abstract and 



TEACHING WRITTEN ARITH.VETIC. 395 

concrete. Abstract problems are designed to illustrate the 
principle, or fix the rule in the mind. The_y serve to make 
pupils read}' and accurate in the mechanical operations. Such 
problems should be suited to the rule they illustrate and the 
capacity of the pupil, being simple at fii*st, and gradually in- 
creasing in difficulty. Concrete problems are the application 
of the abstract principles to something that either does or may 
exist in actual life. These problems should also be adapted 
to the subject and the capacity of the learner. Simple at first, 
they should be gradually complicated until the pupil needs to 
think closely to unravel the complication and attain the 
result. 

Number of Problems. — There should be a large number of 
problems in the course in Written Arithmetic. Principles and 
methods are fixed in the mind by their application, and prob- 
lems are intended for such application. In this respect there 
is a great difference between the French and English works. 
The French have many principles and few problems; the Eng- 
lish fewer principles and more problems. The true method is 
principles and problems, enough of the former, the more the 
better of the latter. Especially should there be a large col- 
lection of problems under the fundamental rules, as the first 
object in the study of arithmetic is to acquire skill in the 
mechanical processes of adding, multiplying, etc. 

Variety of Problems. — Problems should be so varied that 
the solution of one cannot be directly and mechanically 
applied to all the others of the same class. This is an impor- 
tant point. Many teachers who condemn the faults of the old 
schoolmasters in working everything by rule, fall into a simi- 
lar error by requiring pupils to solve everything by " model 
solutions.'' To give a pupil a solution of one of a class of 
problems, and then have him apply it to a dozen others of the 
same class, Avithout any variation or new complication of the 
conditions, so as to require original thought on the part 
of the pupil, is not much better than to solve by the old 



390 METHODS OF TEACHIXG. 

method of '■''the rule says so.''^ Problems should, therefore, 
be A'aried so as to give the pupil opportunity for original 
thought and investigation, that he may become an independ- 
ent reasoner and not a mental parrot. 

Practical Character. — The practical character of the prob- 
lems should be a prominent feature of them. They should 
represent the actual business of the day, and not the scholar's 
idea of what business might be. The problems and processes 
should be derived from actual business transactions, and the 
teacher should endeavor to make this one of the leading char- 
acteristics of his instruction. 

Soliftions and Deinoiistrafionst. — The solutions and demon- 
strations should be simple and clear, that they may be readily 
understood, but at the same time concise and logically accu- 
rate. A solution may be too concise to be readily under- 
stood ; and it may also be too prolix, the idea being smoth- 
ered or concealed in a multiplicity of words. Both of these 
errors should be avoided. There is a language of arithmetical 
science, simple, clear, and concise, as appropriate to the sci- 
ence of numbers as the language of geometry is to the science 
of form. This language is the natural expression of the logi- 
cal evolution of the subject, and should be employed even in 
the most elementary y^rocesses of arithmetic. The teacher 
should always remember that the highest science is the greatest 
simplicity. 

The Rules The rules of arithmetic are statements of the 

methods of operajbion. These rules should be expressed in 
brief and sim))le language, and in a form easily understood by 
the learner. The statement sliould not be too general in its 
terms, but should indicate each step in its natural order. In 
most cases the rule should be derived from the solution of a 
problem, that the pupil may see the'reason for it, and be aV)le 
to derive it himself, as an inference from tlie solution. In some 
cases it is more convenient to state the rule first and then de- 
monstrate it; and this should be done wherever it is seen to 



TEACHING WRITTEN ARITHMETIC. 397 

be preferable. ( With young pupils we should not require the 
rule to be committed to memory, but they should be thor- 
oughly drillerl upon the methods of operation. Older pupils 
should be required to describe the methods, and the study of 
the rules will aid them in doing this. 

Defi,nltlo}is. — The definitions should be clear, concise, and 
accurate. There are two methods of giving definitions, which 
are distinguished as the Inductive and Deductive methods. 
By the Inductive methcjd we pass from the idea to the word ; 
by the Deductive method we pass from the word to the idea. 
Thus, by the Inductive method we would say, "The process 
of fiuding the sum of two or more numbers is Addition;" by 
the Deductive method we would say, " Addition is the process 
of finding the sum of two or more numbers." In the course 
in Primary and Mental Arithmetic, the Inductive method is 
preferred ; in the Written Arithmetic, the Deductive method 
should be used. 

Answers. — The question is often raised whether a text- 
book on Written Arithmetic should contain the answers to 
the problems. We believe that most of the problems should 
have no answers given in the text-book. In case of any pecu- 
liarity in a problem hy which pupils would be liable to obtain 
an incorrect result, the correct answer should be given ; in 
other cases it would I)e better to omit them. In practical life, 
our problems are without answers ; we must determine tlie 
correct results for oui'selves. Education should be disciplin- 
ary for life, hence the pupil should learn to rel}' upon himself 
in studying his text-book. We have no answers in Mental 
Arithmetic, and get along well without them ; could we not do 
as well without them in Written Arithmetic? 

These viewSj however, conflict with the popular view and 
practice. Nearly all teachers prefer having answers to the 
problems in the text-book ; and with elementary classes they 
may be of some practical advantage, to both pupil and teacher. 
Thei'e are some teachers, however, who will not use an arith- 



398 METHODS OF TEACHING. 

raetic with answers; and several authors publish two editions 
of their works, one with and the other without answers, 
so as to meet the wants of all in this respect. 

II. Methods of Teaching Written Arithmetic. As con^ 
ditions for thorough instruction in Written Arithmetic, each 
pupil should be provided with an arithmetic, slate, and pencil. 
In latter times book-slates and scribbling paper have in many 
places superseded slates, and are in some respects preferable 
to the old-fashioned slate. The school-room should also be 
furnished with a blackboard of suitable size and quality. The 
necessity of a blackboard in the school-room is imperative. 
No good teaching can be done without it, especially in 
mathematics. 

Assignment of the Lesson. — The lesson should be assigned 
at the close of each recitation, that the pupil may have time 
to prepare it for the next recitation. In assigning the lesson 
the teacher should be definite as to place and extent, stating 
just where a lesson begins and where it ends, so that there 
can be no doubt about it by the ]iupil. The extent of the les- 
son should be adapted to the ability of the class, care being 
taken that neither too much nor too little be assigned. This 
point is important, for if too little be given, the pupils become 
lazy; if too much, they will become discouraged and disgusted 
with the study. Attention should.also be called to prominent 
points or unusual difficulties, that they may receive special 
attention in the preparation of the lesson. 

PrepatYifiou of the Lesson, — In the preparation of the 
lesson the pupil should be thrown, as far as possible, upon his 
own resources. The teacher should give him no assistance, 
or, at least, very little ; and he should prevent, as far as possi- 
sible, his obtaining any from other mcmlxirs of the class or the 
more advanced pupils. The habit of running to the teacher 
with every little difficulty is a most pernicious one, and de- 
structive of invigorating mental discipline. Independence of 
thought and liold self-relinnce are indispensable traits of man- 



TEACHING WRITTEN ARITHMETIC. 899 

hood, and should be cultivated in the studies of youth, and 
especially in the study of mathematics, Avhich is particularly 
adapted to give such training. 

This point cannot be too strongl}^ urged ; its neglect has 
been productive of much mischief. We have known pu})ils 
who, for a whole session, scarcely ever solved a problem for 
themselves, but prepared their lessons with the aid of other 
pupils. At other times they have obtained notes from those 
who had previously passed over the same subject, and have 
used these notes to the utter neglect of self-thought. It is 
needless to say that much time was thrown away, and that 
such study is worse than useless. Let the pupil, in the pre- 
paration of his lesson, depend mainly upon himself; and what 
he fails to get out in this way, the teacher can explain to him 
at the recitation. 

Tlie Recitation. — The Recitation is the great instrument 
of instruction. In it the teacher comes in contact with the 
mind of the pupil, calls out its energies and moulds it to his 
will. Mind meets mind here — the pupil's mind and the 
teacher's mind — thought is evolved, and mental activity 
stimulated. It is here that the teacher shows his power as a 
teacher, rousing up dormant faculties, directing mental activ- 
ity, and creating interest and enthusiasm in that which was 
before dry and repulsive. 

The method of recitation must be determined by the several 
objects to be attained. These objects, briefly stated, are: 1. 
To find out what the pupil knows of the subject ; 2. To fix the 
subject clearly in the mind ; 3. To cultivate the power of accu- 
rate expression ; 4. To impart instruction. These objects 
should be kept clearh^ before the mind of the teacher to direct 
and inspire his work. 

Method of Recitation. — The lesson being prepared and tJie 
hour of recitation having arrived, the class take their seats 
in the recitation-room for the purpose of reciting. The teacher 
calls the roll to see if all are present, and then proceeds with 



400 METHODS OF TEACHING. 

the recitation, the most important points of which will be 
briefly specified. 

Preparation of the Blackboard. — The first step is the prepa- 
ration of the blackboard. The teacher says, " Prepare the 
board," and the pupils arise and pass orderly to the board, 
erase what work there may be on it, and then divide it into 
equal spaces by vertical lines, each pupil drawing a line to his 
right, and writing his name at the upper part of the sjiace. 
This done, as quietl}' as possible, the pupils turn and stand 
with their backs to the board, and face towards the teacher. 

Assignment of Problems. — The next step is the assignment 
of problems. With young classes the same problem should 
be assigned to all the pupils, or at least one problem to four 
or five pupils ; with advanced classes eacli pupil should receive 
a different problem. If the class is not too large, the problem 
should be read by the teacher, and the pupil be required to 
copy the conditions as he reads. Wlien the class is large, the 
pupils, or at least a part of them, may be permitted to copy 
the problem assigned from the book. They should be required, 
however, to close their books as soon as the conditions are 
written. 

Writing the Problem. — The next step, or one co-ordinate 
with the above, is the copying of the problem upon the board. 
When the problem is abstract, merely requiring an operation 
upon abstract numbei's, the pupil will copy such numbers as 
the teacher reads. If the problem is concrete, involving sev- 
eral conditions, the pupil should be required to mark the 
conditions by a sort of short-hand or abbreviated process 
which he can write rapidly, and which will be readily under- 
stood. He should also write the page and number of the 
problem at the upper part of his space, so that the teacher ma}"" 
readily refer to the y}roblem in the text-book. 

Working the Problem. — The next step is the working of the 
problem upon the board. In this the pupil should practice 
neatness and exactness. The figures should be plainly and 



TEACHING WRITTEN ARITHMETIC. 401 

neatly made. The lines drawn beneath any part of the work 
should be straight and horizontal. The work should gener- 
all3' be written in the form which a person would employ in 
actual calculation. It may sometimes be written in an ana- 
lytic form, the operations and genei-al form of solution being 
indicated by the form of writing. The pupil should be exact 
in such expressions, and not write one thing and mean another. 
Every point, symbol, etc., should be written in its proper 
place, the teacher not being satisfied by the pupil's saying he 
meant so and so, when he had written something else, or 
neglected writing some essential part. Having completed the 
solution of the problem, the pupil should take his seat and 
retain it until called upon by the teacher for his explanation. 

Fodtion at the Board. — In reciting, the pupil should stand 
in an erect and eas}^ attitude, with the pointer in one hand and 
the other hanging down by the side. His side, and not his 
face, should be turned towards the board, so that he can see 
both the solution and the teacher. The teacher should be 
particular upon these points, allowing no awkwardness or 
clownislmess of attitude, but endeavoring to cultivate an 
easy and graceful carriage. At West Point, one of the 
best mathematical schools in the countrj^ they arc ver}"- 
particular upon such points as these, and the effect of it is 
seen in the progress and attainments of the pupils. 

Explanation. — The explanation of the problem should be 
given in a full and natural tone of voice, with great care in re- 
spect to clearness of thought, accuracy of expression, and dis- 
tinctness of enunciation. Those who speak too low should 
be encouraged to speak louder; and those who speak in a loud 
and declamatory style should be taught to speak in a lower 
and more natural tone. If the form of solution is analytical, 
each point should be clearl}' stated as it follows a preceding 
one, care being taken that the whole chain of anal3'sis be 
kept complete. If the solution is deductive, the different 
steps being based upon principles previously explained, these 



402 



METHODS OF TEACHIXG, 



principles should be referred to in their proper order and con- 
nection. The explanation should be clear and full . in all its 
parts, and complete as a logical whole. 

Criticisms. — The pupils who are not engaged at the board 
should be required to observe closely each explanation, notic- 
ing carefully all mistakes in solution, expression, etc. At 
the close of the solution, the class should be called upon for 
correction of errors, suggestion of improvements, etc. The 
character of the solution, whether incorrect, too long, or not 
SLitficiently clear, the form of statement upon the board, posi- 
tion at the board, style of expression, etc., are all legitimate 
subjects of criticism. After the pupils have given their criti- 
cisms, the teacher should present any other suggestions or 
corrections which may be required. At the close of such 
criticisms, the pupil who explained will erase his work upon 
the board, and receive another problem, or take his seat, and 
the next pupil proceed to explain. 

Teacher's Ex-plauation. — It is often necessar}' for the 
teacher to explain some i^rinciple or problem to the class ; the 
proper time of doing this will be suggested by circumstances. 
A principle that several members of the class do not under- 
stand, and which is essential to the lesson to be recited, should 
be explained at the beginning of the recitation. A difficult 
problem should not be explained by the teacher until the 
class have tested their strength with it. It is better to leave 
it for a week or two, to see if the class cannot solve it with- 
out assistance. A spirit of this kind can be cidtivated so 
that pupils will not be willing to have the teacher explain a 
problem until they have assured themselves, by severe labor, 
that it is beyond their powers. Assistance in this respect is 
often better given b}' suggestion than by full explanation. 
This leaves the victory partl}^ theirs, and affords at least a 
partial satisfaction of a triumph. 

New Matter. — For the purpose of exciting a deeper in- 
terest in the subject, the teacher shouUl occasionally intro- 



TEACHING WRITTEN ARITHMETIC. 403 

duce new matter adapted to the comprehension of the class. 
This ma}- be done at the latter part of the recitation hour, or 
he may occasionally occupy the whole period in a lecture 
upon the subject. This will give enlarged A'iews of the sub- 
ject, and awaken the desire of going beyond the limits of 
the text-book used. "With classes sufficienth' advanced, a 
philosopliical discussion of the subject, showing its logical 
evolution from a few fundamental ideas, the relation of the 
different parts to each other, the natural transition from 
Arithmetic to Algebra, the historical development of some 
subject, etc., will be instructive and interesting. 

Iteviews. — We recommend regular reviews. With the 
younger classes, where they are learning merely the mechani- 
cal part, thej' need not be so frequent ; but with other classes 
we suggest a review at the close of each week. In this review, 
less attention may be given to the problems, and more to defi- 
nitions and principles. We should have pupils write anah'ti- 
cal outlines of the week's work, embracing the definitions, 
i:)rinciples, different cases under each subject, etc., in their 
logical order. This will give a comprehensive idea of the 
subject as a whole, and exhibit the logical relation of the parts 
to each other. 

With these suggestions, we close the subject of arithmetical 
instruction, trusting that teachers may realize the full impor- 
tance of the study, and may not only develop in their pupils 
the power of accurate and skillful computation, but train them 
to logical habits of thought and to a full appreciation of the 
beautiful science of numbers. 



CHAPTER VI. 



TEACHING GEOMETRY. 



GEOMETRY is the science of Extension. Extension is 
possible only in space ; hence geometry may also be 
defined as the science of Space. It investigates the proper- 
ties and relations of the ditferent figures that are possible in 
space. These figures have form ; hence geometry treats of 
the forms of space, and has been defined as the science of 
Form. 

Form is of two kinds, Pure Form and Real Form. Pure 
Form is a portion of space limited in thought, but not filled 
with content. Real Form is a portion of space filled with 
some material content. The science of geometry treats of Pure 
Form; but its principles may be applied to Real Form. 

The term Geometry is derived from ge, the earth, and me- 
tron^ a measure; and means literall}^ a measuring of the 
earth, being equivalent to our term, land surveying. It does 
not appear, however, that it ever had simply this significance. 
As far back as we can trace the science, there seems to have 
been a body of truths designated by this terra. Indeed, some 
of the jorinciples ofgeometrj^ must have been known from the 
very beginning of histor3\ 

Nature of Geotneiry. — Geometry is the science of Form. 
Its subject-matter is lines, surfaces, volumes, and angles. 
These genei-al conceptions contain many special forms ; the 
description of these forms gives rise to the definitions of ge- 
ometry. When we consider these special forms of quantity, 
as well as quantity itself, we perceive some truths concerning 
them that are self-evident, that must be true, since they can- 

(404) 



TEACHING GEOMETRY. 405 

not be conceived as untrue. These self-evident truths are 
called the axioms of geometry. 

The science of geometr}' begins with these primary ideas 
of space, and the self-evident truths arising out of them, and 
from these, as a basis, rises to the higher truths l)y a process 
of reasoning. The axioms and definitions are, therefore, said 
to be the basis of the science of geometry. The definitions 
present the subjects upon which we reason ; the axioms give 
some of the truths with which we start, and also the laws 
which guide us in the reasoning process. From these we 
trace our way, step by step, to the loftiest and most beautiful 
truths of the science, by the simple process of comparison. 

Geometry is purely a deductive science. It begins with 
definite ideas giving rise to strictly logical definitions, has its 
fundamental truths or axioms given by Intuition, and with 
these as a basis, proceeds by the logic of deduction to derive 
all the other truths of the science. It is regarded as the most 
perfect model of a deductive science, and is the type and 
model of all science. 

Divisions of Geometry. — Geometry is divided into two 
branches ; Common or Synthetic Geometry, and Higher or 
Analytical Geometry. Common or Synthetic Geometry is 
that which compares geometrical quantities, and derives their 
relations through the ordinary methods of reasoning. It is 
usually restricted to the use of the straight line and the circle ; 
and includes the ordinary plane figures, the rectangular solids, 
and the three round bodies, the cylinder, the cone, and the 
sphere. Analj'tical Geometry is a method of applying alge- 
braic analysis to the investigation of the forms of space. It 
is a general method of investigation that can be applied to all 
kinds of lines, surfaces, and volumes. 

Origin of Geometry. — Geometry is generally supposed to 
have had its origin in Egypt, where the annual overflowing of 
the Nile obliterated the landmarks, and rendered it necessary 
to have recourse to mathematical measurement to re-establish 



406 METHODS OF TEACHING. 

them. This origin is indicated by the terra Geometry, which, 
as stated, signifies the measurement of the earth. But, what- 
ever may have been the origin of the term, the natural tend- 
ency of the human mind to compare things in respect to 
their forms and magnitudes is so universal, that a geometry 
more or less perfect must have existed since the first dawn of 
civilization. 

Geometry, originating in Eg3q)t, is supposed to have been 
introduced into Greece by Thales, who lived about the year 
650 B. C. Pj'thagoras, who lived about 510 B. C, was one 
of the earliest Greek geometers. He is supposed to have dis- 
covered the following principles: 1. Only three plane figures 
can fill up the space about a point; 2. The sum of the angles 
of a triangle equals two right angles; 3. The celebrated prop- 
osition of the square on the hypothenuse. Some say that in 
honor of this last discovery he sacrificed one hundred oxen. 
Plutarch says but one ox; and Cicero doubts even that, as it 
was in opposition to his docti'ines to offer bloody sacrifices, 
and suggests that they ma}^ have been images made of flour 
or clay. 

The next geometer of eminence was Anaxagoras, who com- 
posed a treatise on the quadrature of the circle. Plato, the 
" poetical philosojiher," delighted in the science, and culti- 
vated it with great success, as is proved by his simple and 
elegant solution of the duplication of the cube. About fifty 
years after the time of Plato, Euclid collected the proposi- 
tions which had been discovered by his predecessors, and 
formed of them his famous '■^Elements'' — a work of such emi- 
nent excellence that by many it is regarded, even at the pres- 
ent da3% as the best text-book upon the suliject of Elementarj'- 
Geometry. It consists of fifteen books, thirteen of which are 
known to have been written by Euclid; but the fourteenth 
and fifteenth are supposed to have been added In- Ilypsicles, 
of Alexandria. 

Apollonius, of Perga, about 250 years B. C, composed a 



TEACHING GEOMETRY. 407 

treatise on Conic Sections, in eight books. He is said to have 
given them their names, parabola, ellipse, and hypei'hola. 
About the same time flourished Archimedes, who distin- 
guished himself in Geometry by the discovery of the beautiful 
relation between the sphere and circumscribed cylinder. He is 
also distinguished by his work on conoids and spheroids, by 
his discovery of the exact quadrature of the parabola, and his 
very ingenious approximation to that of the circle. 

Other geometers of eminence followed, among whom the 
most illustrious, perhaps, were Pappus and Diophantus; but 
the Greek geometry, though it was afterwards enriched by 
many new theorems, may be said to have reached its limits in 
the hands of Archimedes and Apollonius, and a long interval 
of seventeen centuries elapsed befoi-e this limit was passed. 
In 1637, Descartes published his Geometry, which contained 
the first systematic application of algebra to the solution of 
geometrical propositions. Soon after this followed the dis- 
cover}'- of the infinitesimal calculus of Leibnitz and Newton; 
and from that time to the present. Geometry has shared in the 
general progress of all mathematical sciences. 

Value of Geometry. — Geometry ranks among the first of 
all studies for the discipline of thought power. It is the perfec- 
tion of logic, and excels in training the mind to logical habits 
of thought. In this respect it is superior to the study of 
Logic itself; for it is logic embodied in the science of form. 
While logic makes ns familiar with the principles of reasoning, 
geometry trains the mind to the habit of reasoning. No study 
is so well adapted to make close and accurate thinkers. Euclid 
has done more to develop the logical faculty of the world than 
any book ever written. It has been the inspiring influence of 
scientific thought for ages, and is one of the corner-stones of 
modern civilization. 

Geometry not only gives mental power, but is a test of 
mental power. The boy who cannot readily master his geome- 
try will never attain to much in the domain of thought. He 



408 METHODS OF TEACHING. 

may have a fine poetic sense that will make a writer or an 
orator ; but he can never reach any eminence in scientific 
thought or philosophic opinion. All the great geniuses in the 
realm of science, as far as is known, had fine mathematical 
abilities. So valuable is geometry as a discipline that many 
lawyers and preachers I'eview their geometry every year in 
order to keep the mind drilled to logical habits of thinking. 

Geometry is of value in all the sciences and arts. " It is," 
says Dr. Hill, " the most useful of all the Sciences." " No 
other science," he adds, " can be learned unless you knoAV 
geometry." It lies at the basis of the sciences of trigonome- 
try, analytical geometry, and the transcendental analysis, 
while the sublime and far-reaching science of astronomy could 
not proceed a step without it. Without geometry, the sci- 
ences of survej'ing and engineering, with all their practical 
results, could have had no existence; and the mechanical skill 
that reared the pyramids or arched the dome of St. Peter's 
would have been impossible. 

Things to be Tauf/Itt. — The things to be taught in geome- 
try are two-fold ; Geometrical Ideas and Geometrical Truths. 
The Geometrical Ideas include the various elements ; as lines, 
surfaces, volumes^ and angles. These embrace all the diff'er- 
ent figures, triangles, quadrilaterals, the circle, polj'edrons, 
cylinders, cones, and the sphere. The Truths of geometry 
are the Axioms and Theorems, the latter of which can be 
api)lied to the solution of practical problems. 

The elements of geometry are simple and readily under- 
stood b}^ children, and should thus be presented ver}' early 
in the course of instruction. Many of the truths can also be 
easily understood and may be taught to 3'oung pupils. The 
reasoning of geometry reqviires considerable mental develop- 
ment, and cannot be understood by children : it should not, 
therefore, as a rule, be presented, before pupils are twelve 
years of age. We shall, therefore, for instruction, divide the 
subject into two parts ; the Elements of Geometry, and Geom- 
etrv as a Science. 



TEACHING GKOMETRY. 409 

I. The Elements of Geometry. 

The Elements of Geometry include all such instruction as 
pupils are prepared for before they are ready to take up the 
subject as a science. These Elements embrace the fundamen- 
tal ideas and truths of the science. The Ideas to be taught 
include a knowledge of all the figures of common geometry, 
their form, nature, parts, and the names of the figures and 
their parts. The Truths to be presented under the Elements 
include some of the axioms and some of the simpler theorems 
of the science. 

Importance. — The importance of a course in the elements 
of geometry will be briefly stated. First, a knowledge of 
geometry is adapted to the young mind. One of the earliest 
ideas of the mind is that of form; objects present themselves 
to us in forms ; and the mind naturally passes from concrete 
form to the conception of abstract or pure form. " The mental 
product in perception is the picture of the object, a picture 
of its form ; and the mind is thus prepared, from the begin- 
ning of its experience, to consider the subject of form. 

Second, the elements of geometry should he taught for their 
practical value. Tae elements of geometry enter into all me- 
clianical operations, and are of use in nearl}' ever}- occupation. 
To omit such a course, as our common schools ^have been do- 
ing, is to send out into the avocations of life people ignorant 
of the simplest principles of mechanics. Such expressions 
heard among mechanics as a " long square," a " slanting 
square," a ''square triangle," a "long circle," etc., show the 
defects of our common schools in respect to this branch. The 
common schools are fitting persons for every avocation ; and 
they should give pupils at least the fundamental principles 
that enter into so many of the practical affairs of life. 

Third, instruction in the elements of geometry lies at the 
basis of drawing. The simplest figures of the drawing lesson 
are the geometrical figures. Drawing should, therefore, begin 
18 



4:0 



METHODS OF TEACHING. 



in geometry; and the elements of geometry may be made a 
stepping-stone to the introduction of drawing into the public 
schools. 

Fourth, lessons in geometry will be of value in school disci- 
jjline. Pupils shonld be required to draw figures on their 
slates, and this will give employment to both minds and fin- 
gers, and keep them out of the mischief that comes from idle- 
ness. In this manner the teacher can reduce mischief into 
geometry, and thus interest and instruct little minds, and 
keep pupils obedient and qniet, because they are busy and 
happy. 

Principles of Teaching. — There are several principles that 
determine the order and methods of teaching the elements of 
geometr}^, wdiich we state briefl_y : 

1. The elements of geometry should precede the elements of 
arithmetic. It has been customary to defer geometry until 
the pupil is quite familiar with the elements of arithmetic, 
but this is a great error in education. The elements of 
geometry are much easier than the elements of arithmetic. 
The ideas of number are much more abstract than the ideas 
of form. The child of four years of age can acquire but a 
very small knowledge of arithmetic, while it ma^' learn to 
distinguish and name nearly all the ordinar}^ geometrical 
forms. 

2. The reasoning of geometry should follow the reasoning 
of arithmetic. Thougli the ideas of Geometry are simpler 
than the ideas of arithmetic, the reasoning of arithmetic is 
much simpler than the reasoning of geometr^^ The former 
is often a mere succession of intuitive judgments, each com- 
parison bearing its evidence in itself; while the reasoning of 
geometry is syllogistic, depending on a principle of inference. 
For this reason the reasoning of geometry should not be in- 
troduced until the pupil has made considerable progress in 
arithmetic. 

3. The method of teaching the elements of geometry should 



TEACHING GKOMETRY. 411 

he concrete. The pupil should see the forms, rather than learn 
to define them. Figures out from pasteboard, models made 
out of wood, diagrams on the board, etc., should be exten- 
sively used in these instructions. Even the truths should be 
illustrated or presented in the concrete, rather than by ab- 
stract demonstration. 

4. The method of teaching should be inductive. The pupil 
should be led to the idea of the different figures and to the dif- 
ferent truths. He should be led to see the distinguishing 
characteristics of figures, the reason why they are named as 
they are; and in mau}^ cases he can be led to appl}' the appro- 
priate term himself by appropriate questions. 

I. The Geometrical Ideas. — The fundamental Ideas of ge- 
ometry are those of the Line, the Su?'face, and the Volume. 
Tliese elements may be reached in two ways, analytically or 
synthetically. We may begin with the idea of a volume, and 
pass from it to the surface and line as elements of it; or we 
may begin with a point, pass to the idea of a line, from the 
line to a surface, and from the surface to a volume. The 
former method is analytic ; the latter is synthetic. 

Analjjtlc 3Iethoil. — We ma^^ present the elements of geo- 
metrical quantity analytically as follows: The teacher may 
take some regular form, as a box, and call attention to it. 
He then takes a rule, and leads the pupils to see that it can be 
measured in three directions ; In length, breadth, and thick- 
ness. He then tells them that these measurements are called 
the dimensions of the box, and leads them to see that it has 
three dimensions, length, breadth, and thickness. 

The next step is to lead them to call it a solid. He leads 
them to call water, because it flows, a fluid; and because the 
hand will not move through the box, as through the water, 
we call the box a solid. He then leads them to conceive of 
the form of the box in space, and shows that tlie hand can 
move through this, therefore, this form is not a solid; from 
which they may see that the better term is volume. They 



412 



METHODS OF TEACHING 



may thus be led to conceive of form in pure space; which is 
the geometrical volume. 

The next step is to teach the idea of a surface. The 
teacher leads them to call a side of a box the surface, and then 
measuring it, shows that a surface has length and breadth. 
He then asks how far they can see into the surface, and thus 
leads them to tlie idea that it has no thickness, but merely the 
two dimensions, lengtli and breadth. 

He then leads them to see that where two surfaces meet, 
since neither has any thickness, tlie edge will have no breadth 
nor thickness, but merely length; and that this is a line. In a 
similar manner, he may show that the end of a line has no 
length, breadth, or thickness, and is called a point. The stu- 
dent-teacher may be required to put this description into 
an inductive lesson. 

Synthetic 3Iefhod. — By the Synthetic Method, we should 
have a pupil conceive a point in space ; then cause this 
point to move, and its imaginary pathway would be a line ; 
then conceive this line to move in the direction opposite its 
length, and it will form a surface ; then conceive this surface 
to move in a certain way, and its motion will form a volume. 

This method is a legitimate one ; the principle of it is 
employed in geometry in the case of the cj'linder, cone, and 
sphere. The analytic method is preferred, however, for sev- 
eral reasons. It is more concrete than the sj'nthetic method, 
as it begins with tliat which can be seen, and not merely con- 
ceived. The synthetic metlxod begins with the most ditlicult 
geometrical conception, a point, which has no dimensions, but 
position onl3% 

Lines. — The pupil has now the general idea of a line; the 
next step is to teach the three kinds of lines, the straight, 
the curved, and the broken line. To do this, take a small 
twig to represent a line ; put it into different forms, leading 
them to name the forms, and then drawing lines to represent 
these forms, have them apply the names to the lines. 



TEACHIXG GEOMETRY. 418 

Model Lesson. — TeacJier. When I pull this stick out straighUvihsLt'km^ 
of a stick is it? Pupil. A straight stick. T. If I draw a line like this 
on the board, what kind of a line is it? P. A straight line. T., bend- 
ing the stick, says, What am I doing to th6 stick? P. Bending it. 
T. When I have bent'ii, what kind of a stick is it? P. A bent stick. 
T. I will place this against the board and draw a line of the same shape; 
what kind of a line is it? P. A hent line. T. Very well; another name 
for this line is curved line T., breaking the stick, says, What am I 
doing with the stick? P. Breaking it. T. When I have broken, it, what 
kind of a stick is it? P. k. broken ?,i\ck. T. I will place it against the 
board, and draw a line like it on the board; what kind of a line shall 
we call it? P. KbrokenYxn^. 

The Angle. — The next step is to give the pupils an idea of 
an angle, and of the several kinds of angles. This may be 
done by taking some object, as a knife, opening it, then plac- 
ing two straight sticks side by side, and making an opening 
lilve an angle, leading tlie pupils to call it an opening ; and 
tlien giving the correct name, have the pupils define an angle. 
Lines on the blackboard may also be used. 

Model Lesson. — Teacher, taking a knife and opening it, asks, What am 
I doing ? Pupils. Opening your knife. T. The space between the blade 
and the handle may be called what? P. The opening. T. I will lay 
two sticks, the one on the other, and open them; what is the space be- 
tween them called ? P. An opening. T. Yes, that is right, but there is 
another name for it; this opening is called an angle. T. What then is 
an angle? P. An angle is the opening bcticeen two lines. The teacher 
will then make angles and require the pupils to make angles on the board. 

Kinds of Angles. — The teacher will then lead the pupils to 
notice the difference between angles, to see that some are sharp 
and others blunt; and that these may be called acute and ob- 
tuse. Then lead them to see that there is one neither sharp 
nor blunt, and which, like a boy who is neither too shar'p nor 
too blunt, is just right, and may therefore be called a right 
angle. The student-teacher will put this into a model lesson. 

Parallel.'^, etc. — We next teach parallel lines, oblique lines, 
converging lines, diverging lines, perpendicular lines, and 
horizontal lines. The method is simple ; the student-teacher 
maj' describe it and give a model lesson. 



414 METHODS OF TEACHING. 

The Triangle, — To teach the Triairgle, give the children 
some little sticks, and liave them make "little pens" with 
them. Tell them to make a pen with five sticks, then with 
four, then with three, then with two; and thus lead them to 
see that three lines is the least number that will enclose a sur- 
face. Then call attention to a figure made with three lines ; 
ask how many angles it has; lead them to call the lines sides; 
then lead them to call it a " three-side, ^^ and then a " three- 
angle,^' and then introduce tri, and lead to the name tri- 
angle. 

Kinds of Triangles. — Then lead them to see that triangles 
differ, and that the different kinds can be named from their 
angles and their sides. Then lead them to name the right-an- 
gled triangle, the obtuse-angled triangle, and the acute-angled 
triangle. Lead also to the different kinds of triangles with 
respect to their sides, and give them the names equilateral, 
isosceles, and scalene. Have tliem draw them on the board, 
and drill them until they are entirely familiar with them. 
Teach also the base and altitude of the triangle. The student- 
teacher will give an inductive lesson on the triangle. 

The Quadrilateral. — Have pupils make a four-sided figure, 
lead them to name it from its angles a four-angle, give the 
word quadra, lead to quadrangle, its proper name. Then 
lead them to name it from its sides a four-side ; introduce 
lateral for side, and quadra for four, and lead to quadri- 
lateral. Then lead them to discover the three classes of 
quadrilaterals; and give the names parallelogram, trapezoid, 
and trapezium. Then lead them to discover the several kinds 
of parallelograms ; the rectangle, square, rhombus, and rhom- 
boid. The subject will admit of a beautiful inductive devel- 
opment, which the student-teacher will give. 

Polygons, — We should then give a general lesson on Foli/- 
go7is, including the pentagon, hexagon, heptagon, etc. We 
should teach the meaning of perimeter, area, regular and 
irregular polygons, their division into triangles, etc. 



TEACHING GEOMETRY. 415 

Thd Circle. — TVe should ucxt te.acli the Circle^ including 
the circumference^ semi-circumference^ quadrant^ arc, diam- 
eter, radius, chord, sector, segment, tangent, etc. We should 
show pupils how to construct the circle, and require them to 
draw and name the different parts. Attention may be called 
to the difference between the circle and the circumference, 
which are often confounded. The use of the circumference 
in measuring angles may also be explained, and the division 
of the circumference into degrees, minutes, and seconds. 
Pupils maj^ also be taught to inscribe squares in circles, and 
circles in squares, etc. They may also be shown how to in- 
scribe a regular hexagon by taking the radius as a side; and 
also how to form an inscribed triangle from the inscribed 
hexagon. The student-teacher will give a model lesson on 
the circle. 

Volumes. — Among the Volumes we should first teach the 
cube, the pijramid, the cylinder, the cone, and the sphere, 
We next teach the prism, and the different kinds of prisms, 
named from the form of the bases. We should next teach the 
oblique and right 2:>risms, the parallelopipedons, rectangular 
parallelopipedons, the frustum of a pyramid, frustum of a 
cone, etc. We should have models of these different volumes, 
and also draw them and show pupils how to draw them on 
the board. 

Round Bodies We may then give a more detailed lesson 

on the three round bodies, the Cylinder, the Cone, and the 
Sphere. We may show that the cylinder can be generated by 
the revolution of a rectangle ; explain which is the base, the 
altitude, and the convex surface. We may show how a cone 
can be generated by the revolution of a right-angled triangle 
about one of its sides, and explain the 6a.se, altitude, slant 
height, and convex surface. We may show how a sphere can 
be generated by the revolution of a semicircle around the 
diameter, and explain the diameter, radius, convex surface, 
small circles of the sphere, gi'eat circles, spherical triangles, 
spherical polygons, the lune, etc. 



416 METHODS OF TEACHING. 

We mention in detail the things to be taught, so that 3'Oiing 
teachers may have a clear conception of the course suggested. 
They should be prepared on the subject themselves, and then 
know how to present it in an interesting manner. Let the 
student teacher be required to present a model lesson on each 
one of the figures. 

II. The Geometrical Truths. — Children may also learn 
many of the truths of geometry as well as the ideas. The 
truths of geometry are of two kinds; those that are self-evi- 
dent, called axioms, and those that are derived by demonstra- 
tions, called theorems. 

Many of the self-evident truths of geometry are readily 
understood by young pupils. Many of the theorems may be 
illustrated or presented by what might be called a concrete 
demonstration. An abstract or logical demonstration of them 
would be too difficult for children, and nothing of the kind 
should be attempted. Some of the other trutlis which cannot 
be illustrated may be taken on faith ; the pupils accepting 
them, not because they can see a reason for them, but because 
the teacher tells them they are true. 

Self-evident Truths — Little children may readily be led 
to see that "A straight line is the shortest distance from one 
point to another." Unite two points with a straight line, a 
curved line, and a broken line, and the}^ will see l)y intuition 
that the straight line is the shortest route. To make it inter- 
esting, have them suppose three little boys start from the 
same point to travel on three lines, and they will readily see 
which has the shortest road to travel. The ancients used to 
say that a donkey knew that one side of a triangle was 
shorter than the sum of the other two sides, for he would go 
straight across from one corner of a field to the other, rather 
than follow the two sides of the field. 

They may also be taught to see that " two right angles are 
equal to one another." Care should be taken that they see 
that the size of the angle depends on the extent of the open- 



TEACHING GEOMETRY. 417 

ing, and not on the length of the sides. The}' may also read- 
ily see that "the diameters of the same circle are all equal;" 
that " the radii are all equal ;'' that "the i-adius is half the 
diameter," etc. In fact, they may be taught nearly all the 
geometrical axioms. The student-teaeher will present the 
lesson. 

Truths by Conct'etc Demonstration. — Mau}^ of the truths 
of geometry can be taught b}' concrete demonstration. That 
is, they may be illustrated in such a way that pupils can be 
assured of their truthfulness without depending upon the 
statement of the book or the teacher. We will give a list of 
such theorems, and suggestions for their illustration. 

1. If one straight line meet another straight line, the suvi 
of the two adjacent angles equals two right angles. Take two 
straight sticks, A and B ; place the end of A neai- the middle 
of B, perpendicular to it ; then will be formed two right an- 
gles. Then incline the stick A, and the pupil can see that one 
angle loses what the other gains, and that they both just fill 
up the space of two right angles, and hence are always equal 
to two right angles. Illustrate the same also on t-he board. 

2. All the angles formed on one side of a straight line by 
drawing lines from the same point, are equal to two right 
angles. This can be shown as in the previous theorem, and 
the pupil may illustrate it on the board. 

3. The sum of the three angles of a plane triangle is equal 
to two right angles. To illusti'ate this, cut out a triangle from 
stiff paper of any form ; then cut off two of the angles, and 
place one on each side of the third angle, and it will be found 
that they just fill up the angular space of two right angles. 

4. If two triangles have two sides and the included angle of 
one respectively equal to two sides and the included angle of 
the other, the two triangles are equal. To show this, cut out 
of paper a triangle of any shape ; then mark out on another 
piece of paper two sides and an included angle equal to those 
of the given triangle, then draw a straight line uniting the 

18* 



418 METHODS OF TEACHING. 

extremities of the sides, cut out the triangle, and compare 
them bj^ placing one on the other, and it will be found that 
they exactly coincide. 

5. The area of a rectangle equals the number of units in 
the base multiplied by the number of units in the altitude. 
Take any number of square blocks, as five, and pile them up 
in three rows of five each, forming a rectangle. The whole 
surface of the rectangle is formed by the one side of the square 
blocks, and since there are 5 in a row, and 3 rows, there are 
3 times 5, or 15, in all; hence the product of the number of 
units in the base multiplied hy the number of units in the 
height, will give the whole number of square units in the sur- 
lace.' Illustrate it also on the blackboard. 

6. The area of a parallelogram is equal to the lyroduct of 
the base and altitude. Cut out a paper parallelogram, cut off 
one corner vertically across ; put this triangle on the other 
end of the parallelogram, and it will become a rectangle. Now 
the surface of this rectangle is precisely the same as the sur- 
face of the parallelogram, and its base and altitude are the 
same. But the area of this rectangle is equal to the product 
of the base and altitude ; hence the ai-ea of the parallelogram 
is equal to the product of the base and altitude. 

7. The area of a triangle equals the product of the base by 
half the altitude. Cut out a parallelogram; then divide' it 
into two triangles, cutting across from one corner to the other. 
These two triangles are equal, and hence equal to one-half of 
the parallelogram, and hence to one-half of the product of the 
base multiplied by the altitude, 

8. The area of a trapezoid is equal to the sum of the two 
parallel sides multiplied by half the altitude. This can be 
shown by cutting out a trapezoid, dividing it into two tri- 
angles, showing that the area of each equals its base into one- 
half of its altitude, and that their sum will be the sum of the 
two bases into one-half of the altitude. 

9. The square on tJie hypothenuse of a right-angled tri- 



TEACHING GEOMETRy. 419 

angle is equal to the suvi of the squares on the other two sides. 
Make a right-angled triangle on the board, one side 3 and the 
other side 4, the hypotheuuse will be 5 ; construct squares on 
each, and divide them into small squares; the square on one 
side will contain 9, that on the other 16, and that on the 
hypothenuse 25; and 25 we see is the sum of 9 and 16. Here 
we see that the square on the hj'pothenuse is equal to the sum 
of the squares on the other two sides. 

Many other truths can be taught in this way ; and such a 
concrete considei-ation of the subject will be a valuable prep- 
aration for the study of the subject abstractl3^ Let the 
student-teacher give a lesson on each one of these, using 
paper and the blackboard. 

III. Truths to be Taken on Faith. — We should teach the 
pupils of the common school some truths that cannot be illus- 
trated to them. Such truths they may take on faith ; pupils 
believing them as they do the facts of geography and historj^, 
because the teacher states them as true. This instruction 
may extend to curves not treated of in ordinary geom- 
etry, including the Parabola, the Ellipse, the Hyperbola, the 
Cycloid, the Catenary, etc. 

Ill Ordinary Geometry. — It will be well to teach the more 
advanced pupils how to find the circumference of the circle by 
multiplying the diameter by 3.1416, to find the area by multi- 
plying the circumference by half the radius; that an angle 
at the centre is measured by the arc included between its sides; 
that an angle at the circumference is measured by one-half 
the arc included between its sides; how to find the volume of 
a prism, the convex surface and volume of a cylinder, the 
volume and convex surface of a pyramid and a cone, the sur- 
face and volume of a sphere. These should be introduced as 
they are prepai'ed for them, the pupils being drilled on their 
application, but no attempt being made to explain the reason 
for them. 

The Par(il)(>l<f. — If a cone be cut by a plane parallel to its 



420 



METHODS OF TEACHIXa. 



slanting sides, the section formed is a beautiful curve called a 
Parabola. This is a very interesting curve. Ever}' stone that 
a little boy throws at an object forms a parabola in its flight. 
In a snow-balling match, all the balls form parabolic curves ; 
and in a battle, shot and shell go humming and sci'eechins: 
through the air in parabolic arcs. It may be well to show 
that the area of a section of this curve is two-thirds of the base 
inultiplied by the altitude. This area may be compared with 
the area of a rectangle and triangle of the same base and alti- 
tude. The method of constructing a parabola should also be 
given. 

The Ellipse. — If a cone be cut by a plane making an angle 
with the base less than that made by the side of the cone, the 
result will be a closed curve that looks like a circle drawn out. 
Such a curve is called an Ellipse. This curve can be made 
by driving two pins in a board, and tying a string at each end 
to one of these pins, and then putting a pencil point inside 
the sti'ing, stretching it out and moving it round. A doubled 
string passed around the pins is still better. The two points 
at the pins are called the foci of the ellipse. The point be- 
tween these is the centre, a line through the foci is called the 
major axis ; and a line perpendicular to this through the cen- 
tre is the minor axis. 

The ellipse is also an interesting curve. The earth in its 
march around the sun follows a pathway of the form of an 
ellipse, the sun being in one of the foci of the elliptical orbit. 
The moon moves around the earth in an ellipse, and all the 
planets and satellites move in the same curve. To find the 
area of an ellipse, we multiply the half of the two axes together, 
and that product by 3.1416. Another interesting fact is that 
if we had a mirror in the form of an ellipse, a light placed at 
one focus would have its rays all reflected in the other focus ; 
and if we had a whispering gallery in this form, a whisper at 
one focus would be distinctly heard at the other focus. 

The Hyperbola — If a cone be cut b}^ a plane making a 



TEACHING GEOMETRY. 42] 

larger angle with the base than the slanting side makes with 
it, the curve formed is an Hyperbola. If we tie strings at dif- 
ferent points of a horizontal wire, and draw them all through 
a point below the wire and cut them off at the point, when 
they hang down straight their ends will form an hyperbola. 
If we tie threads to each link of a hanging chain, and cut off 
their ends in a level line, and then draw the chain out hori- 
zontal, the lower ends of the threads will form an h3'per- 
bola. There are man}^ interesting truths concerning the 
hyperbola. 

The Cycloid. — If a wagon wheel roll on a level floor, a nail 
in the tire or rim will make a series of curves, each called a 
Cycloid. A boy can make a cycloid by fastening a pencil to a 
spool and rolling the spool slowly against the inside of the 
frame of his slate. There are several interesting properties of 
the cj^cloid. 

1. The height of the cycloid at the middle is equal to the 
diameter of the wheel or circle which formed it. 2. The 
length of the straight line joining the two ends of the curve, 
called the &a.se, is equal to the circumference of the generat- 
ing circle. 3. The length of the curve is four times the diam- 
eter of the generating circle. 4. The area of the curve is equal 
to three times the area of the generating circle. When the 
circle is at the middle of the cycloid, the curious looking 
three-cornered figures on each side of the circle are each 
exactly as large as the circle itself. 

5. If a cycloid is turned upside down, a ball will roll down 
it quicker than on anj-- other curve : for this reason the 
cycloid is called the curve of swiftest descent. If a hill were 
hollowed out in the form of a cycloid, a sled would run down 
it faster than if it were of any other shape. 

6. Another curious property is that if several balls start at 
different points on the curve at the same moment, they will all 
reach the bottom at the same time; so that it is also the curve 
of equal descent. 



422 METHODS OF TEACIIIXG. 

The Catenary. — When a chain hangs from two posts, it 
makes an interesting curve, called a Catenary. A jumping 
rope, a clothes-line, and a gate chain, all hang in the form of 
a catenar}'. The curve was first noticed hy Galileo, who 
thought it was the same as the parabola. Its true nature was 
first demonstrated by James Bernoulli. This curve has also 
several curious properties. 

1. If the chain were made of a great many short pieces of 
wood or metal hinged together by rivets, like tlie inside chain 
of a watch, and we could turn it up in the same form it has 
when it hangs, it would stand up without falling in, and be a 
catenary upside down. This is tlie only curve that possesses 
this property. 2. If we wish to make the strongest possible 
arch for a bridge, we should make it in the form of a cate- 
nary. 

For other facts in the elements of geometry, see First Les- 
sons in Geometry^ b}- Dr. Thomas Hill, a valuable little book. 

II. Geometry as a Science. 

The previous course in the elements of Geometrj'^ is de- 
signed as an introduction to the study of the subject as a 
science. By means of it, pupils will become familiar with the 
leading ideas and truths of geometry, and thus be prepared 
for a more intelligent study of the science when of a suitable 
age. Pupils may begin the stud}'^ of geometry as a science 
when about thirteen or fourteen years of age. 

I. The Nature of the Study. — The stud}^ of Geometry as 
a science includes Defimtions^ Axioms^ Postulates, Theorems, 
Demonstrations, Problems, Solutions, and Applications. We 
shall speak of the nature and methods of teaching each of 
these, and also of the method of hearing a recitation in 
geometrj', 

Definitions. — The Definitions of geometry are statements 
of the ideas of tlie science, or a descri[)tion of the quantities 
iipon which we reason. They are exam[)los of wliat are known 



TEACHING GEOMETRY, 423 

as logical definitions ; that is, they define by genus and cZt/Zer- 
e??iia, or specific difference. Thus, in the definition, ''A tri- 
angle is a polygon of three sides," polygon is the generic 
term, and three sides is the differentia or specific difference. 
No science presents so many fine examples of logical defini- 
tions as geometry. 

These definitions shonld be expressed in the deductive 
form; that is, we should begin with the term to be defined, 
and pass to genus and differentia. The definitions should be 
stated positively, not negativel}^, telling what a thing is, and 
not what it is not. Thus, the old definition, "A straight line 
is one that does not change its direction," etc., is not as satis- 
factory as the positive one, "A straight line is one that lies 
in the same direction," etc. 

Hoiv Teach. — In teaching the definitions, the first requisite 
is that the pupils have a clear notion of the thing defined. 
They should be required to give an illustration of each defini- 
tion in which there may be the least difficulty. This point is 
important, as pupils are often found trying to reason from a 
definition when they have no clear idea of the quantity de- 
fined. It is especially necessaiy with pupils of good memory, 
who are apt to rest satisfied with a form of Avords without 
taking the trouble to see clearly what is meant by them. 

Care should be taken to see that the definitions, as given by 
the pupil, are strictly accurate. The language of the author 
should be insisted upon, unless the teacher or pupil can im- 
prove the definition, which, in such a science as geometry, 
will be seldom possible. Most of the definitions are classic 
with culture and age, and have become fixed in form, and will 
not admit of improvement. It is an excellent exercise to 
show, by question and illustration, the importance of the 
prominent points of a definition, and how any departure from 
the statement will vitiate the correctness of the definition. 
A proper study of the definitions of geometry may be made 
a source of excellent mental discipline. 



/24 METHODS OF TEACHING. 

Aocionis. — The Axioms of geometry are the self-evident 
truths which pertain to the subject. These truths lie at the 
basis of the science; they are the foundation upon which all 
the other truths rest. They express the fundamental and 
necessary relations of quantity, and depend for their existence 
on no truths which lie behind them. These truths are intu- 
itive ; they are not the result of reasoning. The mind is so 
constituted that it knows them to be true upon the mere an- 
nouncement or contemplation of them, and neither asks nor 
needs any proof of them. 

Two Kinds. — There are two kinds of axioms in geometry; 
those which pertain to quantity in general, and those which 
grow out of the particular quantity considered. Examples 
of the former class are, " Things that are equal to the same 
thing are equal to one another;" "If equal quantities be 
equally increased or diminished, the results will be equal." 
These apph^ to arithmetic and algebra, as well as to geometry. 
Examples of the second class are, " All right angles are equal 
to one another;" "The radii of a circle are all equal." These 
arise out of the particular kind of quantity considered, and 
apply only to geometry. 

Their Use. — The use of axioms in reasoning, as usually 
stated, is that they are general truths ivhich contain all the 
jjarticular truths of the science. According to this view, the 
geometer needs onl}' to analyze the axioms, and he will find in 
them all the truths of the science. In reasoning, he only un- 
folds these general truths and evolves the special truths which 
he finds contained in them. This view of the subject admits 
of question. It may be pleasant for one to suppose that 
when he knows the axioms of a science, he has in his mind, 
potentially if not actually, the entire science; but it does not 
seem to express a scientific truth. A general formula may 
truly be said to contain man}' special truths which may be 
derived from it; but no axiom iii^this sense can be named that 
contains the other truths of geometry. 



TEACHING GEOMETRY. 425 

Another view is that axioms are the laics ivhich guide us in 
7-easo)iing: they are the Inivs of comparison or inference. 
Thus, if we wish to compare A and B, seeing no relation 
directly between them, we may compare each to C ; and prov- 
ing that they are both equal to C, we infer that they are equal 
to each other. The law that governs this comparison, and 
enables ns to make the inference, is the axiom, Things that 
are equal to the same thing are equal to one another. So in 
comparing parts of the circle, we must always bear in mind 
the truth that the radius is half of the diameter ; but it can- 
not be trul}'' said that this axiom contains other truths. 

It is also true that an axiom may be one of the premises of a 
sjdlogism from which a conclusion is drawn. Thus in a dem- 
onstration we may see a line A equal to a radius B of a circle, 
but radius B is equal to radius C of the same circle; there- 
fore, this line A is equal to radius C. In this case the axiom 
of equal radii is neither a general truth containing other 
truths nor a law of reasoning. Axioms may thus perform 
several offices in a demonstration ; but they are alwa3's first 
truths, beyond which we cannot go in thought. 

Hoiv Teach. — In teaching the axioms, the pupil should be 
required to give an exact statement in the language of the 
book, unless it can be improved. No awkward or half-way 
statement should be accepted as satisfixctory. He should also 
be required to illustrate the axiom, that the teacher may be 
sure he has a clear conception of the truth he is stating. 

JPosfulafes. — An axiom may be defined as a self-evident 
theorem. A self-evident proV)lem is called a Postulate. Thus 
it will be granted that "a straight line may be drawn from 
one point to another," or that "two lines may be constructed 
ecjual to each other." The postulates bear the same relation 
to problems that axioms do to theorems. The same remarks 
will applj' to the teaching of them that we have already made 
with respect to teaching axioms. 

Reasoning. — All reasoning is the comparison of two ideas 



426 METHODS OF TEACIIIXG. 

through their relation to a third. Thus, suppose I see no re- 
lation between A and B,but upon looking at a third quantity, 
C, I perceive that A equals C, and also that B equals C; and 
I can then infer that A equals B. I tlius compare A and B 
through their common relation to the third quantity, C; C 
thus stands intermediate between A and B, and the process is 
called a process of mediate or indirect comparison. 

This is the general nature of the reasoning of geometry. 
In its application to geometry reasoning assumes two differ- 
ent forms, which ma}' be distinguished as the analytic and 
synthetic methods. The analytic method is adapted to the 
discovery of truth ; the synthetic method is used in proving 
a truth when it has already been discovered. 

Synthetic Method. — The Synthetic Method of proving a- 
truth already known is called demonstration. Demonstration 
begins with self-evident truths or truths alread}' proved ; and 
passes, step by step, to the truth to be proved. There are 
two distinct methods of demonstration. The simplest form 
is that in which figures are directly compared by appl3'ing one 
to another. This is called the method by superposition. It 
is used in proving the equality of polygons and also of some 
of the volumes. The more general form of demonstration is 
that in which truths are i^roved by a reference to the defini- 
tions and axioms, or to some principle previously proved. 

Analytic Method. — The Analytic Method begins with the 
thing required, and traces the relation between the various 
elements, till we arrive at some known truth. It is a kind of 
going back from the result sought, by a chain of relations, to 
what has been previously established. In the synthetic 
method, we pass through every step, from the simplest self- 
evident truth to the highest truth of the science. In the 
process of analysis, we pass over the same i)ath, descending 
from the higher truths to the simpler and fundamental truths. 

Analysis is the metliod of discovery; syntliesis is the 
method of presentation. The one has for its object to find 



TEACHING GEO.\!ETRY. 497 

unknown truths ; the other to prove known trutlis. Fre- 
quentl}^ both methods are employed simnltaneously, when the 
object is to discover new theorems, or to find the solution of 
new problems ; but when we wish to prove to others the truths 
alread}^ known, the synthetical method is usually preferred. 

Reductio ad Abaurdum. — There is a form of reasoning 
which is analytic in its character, known as the reductio ad 
absurdum. It consists in supposing that the proposition to 
be proved is not true, and then showing that such a hypotkc- 
sis leads to a contradiction of some known truth. This proves 
a theorem to be true by simply showing that it cannot be 
false. The method is frequently used to prove the converse 
of a proposition, when there is no good direct method; it is 
also used in treating incommensurable quantities. 

This method of reasoning is also called a demonstration ; 
and is called the Indirect Method, to distinguish it from the 
other, which is called the Direct Method. The indirect 
method is not considered as satisfactory as the direct method, 
and should never be used except when no good direct method 
can be found. 

Errors in Reasoning. — There are two errors in reasoning 
into which young geometricians are liable to fall. The first is 
called Reasoning in a Circle; the second is called Begging the 
Question. We reason in a circle, when, in demonstrating a 
truth, we employ a second truth which cannot be proved with- 
out the aid of the truth we are trying to demonstrate. We are 
said to beg the question, when, in order to establish a proposi- 
tion, we employ the proposition itself. 

Practical Problems. — A radical defect of most of our 
lext-books on geometry is that they present the subject so 
abstractly that when the pupil has completed his course, he is 
often unable to make any practical application of what he has 
learned. This defect can be supplied by requix'ing the pupils 
to apply the principles of the science to practical examples. 
Such applications will show them the use of the principles, 



428 METHODS OF TEACHING. 

and they will thus understand it better and remember it 
longer. They will also place a higher value on the science on 
account of their being able to apply their knowledge to some 
practical purpose. These applications will also add an inter- 
est to the study that it cannot possess by the purely abstract 
method. Every text-book in geometry should be supplied 
with a large collection of practical examples. 

Undemonstrated Theorems. — Another defect in the teach- 
ing of geometry has been the lack of matter for original 
thought. The study as usually pursued does not give train- 
ing to the inventive powers of the student. He is required to 
learn the demonstrations of the text-book, but he has no 
undemonstrated theorems to test his own geometrical powers 
and to ti'ain him to reason independently of the text-book. 
To remedy this defect, he should be given a collection of 
theorems for original thought^ and be required to try his 
powers of reasoning in finding out the demonstration for 
himself. 

These theorems should be eas}^ at first, and graduallj' in- 
crease in difficulty as the pupil gains strength for the work. 
They may be mingled with the propositions of each book 
(geometry is usually divided into a number of books), or they 
may be placed at the close of each book. The latter method 
is preferred with most pupils, as they should be quite familiar 
with the propositions of anj' given book before they are pre- 
pared to apply these principles to the investigation of other 
truths. One original theorem each day to apply the prin- 
ciples gone over, in connection with two or three theorems of 
the following book, will make a very interesting exercise. At 
the close of the text-book, there should be a large number of 
miscellaneous theorems for original thought. 

This is the method used in arithmetic and algebra, and it 
seems surprising that it has not been more generally em- 
ployed in geometry. Several authors seem recently to have 
realized the importance of such exercises, and have occasion- 



TEACHIXG GKOMETRY. 429 

ally given some practical problems, and, in one or two in- 
stances, a collection of undemonstrated theorems. In the 
anthor's work on geometry, such problems and theorems are 
a prominent and essential part of the plan. 

II. The Recitation. — The several things to consider under 
the recitation in geometry are: 1. The assignment of the 
theorems ; 2. The construction of the diagrams ; 3. The dem- 
onstration ; 4. The criticism ; 5. New matter. 

Assignment. — The theorems may be assigned to the pui)ils 
in various waj's. They may be given out at random, without 
any reference to the ability of the class; or, if there are some 
in the class who are not very strong in the branch, the easier 
propositions may be given to them. The best way probably 
is to assign by chance, which may be done by writing the 
numbers of the propositions on small pieces of paper, and re- 
quiring the pupils to draw these papers. It is suggested that 
at least one day's review lesson should be included in each 
recitation, the class taking three or four propositions in ad- 
vance, and the same number in review. 

Construction. — The pupil having received a theorem, 
should be required to go to the board and construct the dia- 
gram without an\' reference to the book. The lines should be 
drawn by free hand, and not with the aid of a ruler. The 
letters of the diagram should be placed at random, and dif- 
ferent from the order in the book, in order to prevent a recita- 
tion from memoiy. Figures in place of letters ma}- often be 
used in marking the diagrams. It will add interest also for 
one pupil to construct the diagram for another pnpil, each 
thus constructing the figures of one proposition, and demon- 
strating another. 

Deniothstration. — In demonstrating the theorems, the 
pupil should stand at the board in an erect and easy attitude, 
his face turned partly toward the class, and the pointer being 
in the hand next to the board. The theorem should first be 
stated clearly and precisely, and in the language of the book, 



430 i^IETIIODS OF TEACIIIXG. 

unless it can be equaled or improved. The demonstration 
should be clearly and logically presented, the definitions and 
axioms referred to by number or, with beginners, b^^ rejjeti- 
tion, and previous theorems referred to b}' number of book 
and theorem. When the demonstration involves several pro- 
portions, these may be written out on the board and be 
pointed at in the demonstration. 

It will be well also for the pupil to write out an anal3^sis of 
the course of reasoning involved in a demonstration. Some- 
times an analysis merely of the references or dependent truths 
may be written. Sometimes the pupil may be required to 
write an anal3^sis of all the principles involved in the demon- 
stration, tracing each truth all the wa^- back to the definitions 
and axioms. Such an exercise will be found most valuable in 
giving pupils a thorough knowledge of the subject. 

Criticism. — At the close of the recitation of any pupil, 
the members of the class who have observed any errors may 
be called upon to point them out. These may consist of the 
omission of necessary links in the chain of reasoning, the 
omission or misquoting of references, etc., etc. Pupils who 
have a shorter or better, or even a different method, may be 
called upon to give it. Errors unnoticed by the pupils, may 
then be pointed out by the teacher. 

Qnestioiiitu/ — The teacher should quiz the pupil on his 
demonstration. He should ask questions like the following : 
What kind of a demonstration is it? Why do j'ou begin as 
you do? Why do you prove such a thing equal to such a 
thing ? What relation does this proposition bear to the pre- 
ceding proposition? What application can you make of this 
truth? etc. 

Otfflines. — At the'close of a book, the pupil should be re- 
quired to give an outline of the book; show the design of 
it; show what propositions reach final truths, and what prop- 
ositions were merel}^ auxiliary ; show the relation of each 
proposition to the chain of logic, and how the chain would 



TEACHING GEOMETRY. 431 

be broken b\' the omission of any proposition; etc. B3' fol- 
lowing" these suggestions, the tcMcher will make geometry a 
delightful stud}^ to his pupils, and a most valuable means of 
mental culture. 

New Maftcr. — If the teacher has any new matter, it may 
be i)resented at this time. He may give a discussion of the 
general nature of the lesson, show the excellence or defect of 
the method of development made use of, and make a compar- 
ison between the method of treatment used b}'^ the author and 
that of other authors. He should then assign the next les- 
son, and present any suggestions concerning it that may 
seem advisable. 

Conclusiou. — In conclusion, we would urge teachers to 
introduce the elements of geometry into our public schools. 
A little less arithmetic, if need be, in order to present some 
georaetr}', would be an advantage. We trust that teachers may 
realize the importance of the subject, and endeavor to awaken 
a deeper interest in the beautiful science of form — a science 
over which the ancient sages mused with such deep enthu- 
siasm, and to which the achievements of modern art and 
invention are so largely indebted. 



CHAPTER VII. 



TEACHING ALGEBEA. 



4 LGEBRA is that branch of mathematics which inves- 
i L tigates quantity l\v means of general cliaracters called 
symbols. The term originated with the Arabs, and comes 
from al-gabr, a reduction of parts to a whole. The definition 
given states the general character of the subject, tliough it is 
difficult to give a definition, that fixes preciselj^ts province 
and object. 

Relation to Arithnietic. — Algebra in its elements is closely 
related to arithmetic. It had its origin in arithmetic, and its 
fundamental ideas and operations are arithmetical. Its sj'm- 
bols of quantity were at first merely general symbols of num- 
bers, and its fundamental operations of addition, subtraction, 
etc., were entirely similar to those of arithmetic. On account 
of this relation, algebra has been called a kind of general arith- 
metic. Newton called it Universal Arithmetic. P'Alembert 
regards it as a special branch of the general science of num- 
bei's ; and divides arithmetic into Numerique, special arith- 
metic, and Algehre^ general arithmetic. 

Ifidev View. — This view of the nature of algebra is now 
t )0 narrow. Algebra has transcended the bounds of its ori- 
gin. It reaches from arithmetic over into geometry, including 
continuous as well as discrete quantity. From the generality 
of its symbols, also, many ideas and processes arise which have 
no meaning or use in arithmetic ; as negative and imaginary 
quantities, the solution of higher equations, etc. 

Another important difference is, that in arithmetic the com- 
putations being made as tliey arise, all traces of the interme- 
diate steps are lost, and the result is applicable to a single 
case only; whereas in algebra the result is general, and con- 

(482) 



TEACHING ALGEBRA. 438 

tains implicitl}^ the answer to all problems of the same general 
class. The combination of algebraic symbols leads to expres- 
sions called fonnalas^ in which the operations are indicated 
rather than performed, aiKl whicli admit of interpretation. 
These formulas often express a general truth corresponding 
to a theorem, which arithmetic can verify in particular cases ; 
as (a-\-b)(a — b) = a~ — 6-, and x=^ — iidczs/q-j-p'^, 

Cointe's View. — Comte divides mathematics into geometry- 
and analysis or calculus. Calculus embraces algebraic calcu- 
lus, or algebra, and arithmetical calculus, or arithmetic. Al- 
gebra is defined " as having for its object the resolution of 
equations,''^ which signifies " the transformation of implicit 
functions into equivalent explicit ones." Arithmetic is defined 
as the science which " ascertains the values of functions.'^ 
"Algebra is the calculus of functions ;" and "Arithmetic is 
the calculus of values.^' Sir William Rowan Hamilton, the 
author of Quaternions, defines algebra as the science of time, 
which De Morgan changes to the calculus of succession. 

Sumhols. — The symbols of algebra are of three general 
classes ; Symbols of Quantity, Symbols of Relation, and Sym- 
bols of Operation. The S^-mbols of Quantity are of two 
kinds; symbols of known quantities and symbols of ujiknown 
quantities. They include also the two limits of quantity, 
zero, 0, and infinity, oo. The Symbols of Operation include 
the signs of all the operations to which quantity can be sub- 
jected. The Symbols of Relation include the symbols which 
arise in comparing quantity; as, =,:,::,>•<;, etc. 

The symbols of quantity apply to continuous as well as dis- 
crete quantity. Thus a and b may represent two lines as well 
as two numbers. If these lines have a common unit, then a 
and b may be regarded as representing the lines numericalhi ; 
but when the lines have no common unit, a and b denote them 
as continmous, and not as discrete quantity. 

Generalization. — The spirit of generalization in algebra is 
the source of man}- of its ideas and processes. From this we 
19 



434: METHODS OF TEACIIINQ, 

have the negative quantity, the fractional and negative expo- 
nent, the imaginary quantity, etc., each of which admits of 
explanation and leads to new conceptions in the science. 
Thus, the sign of subtraction is primarily used to denote that 
a quantity is to be subtracted ; but if we subtract a from the 
quantity a — h, we have a remainder of — b, the interpretation 
of which gives us the idea of a Negative Quantity. 

The Fractional Exponent originates in the same way. Hav- 
ing agreed to indicate a power by an exponent, by generaliza- 
tion we have a"; and since n can repi-esent any quantit}^, it 
may represent a fraction, as |,and we have a"^. This expi-es- 
sion being interpreted, we find means the third power of the 
fourth root of a. Or, having the rule that the root of a quan- 
tity may be obtained by dividing its exponent, in extracting 
the 4th root of a^ we reach the same result, a*. 

The Negative Exponent has a similar origin. Since the 
general exponent may represent any quantity, it may repre 
sent a negative quantity, and we may thus have a~^ ; a new 
idea which needs interpretation. Or, if we divide a,^ by a^" 
according to the general rules of division, we also reach the 
expression a— '* ; and this we find denotes the reciprocal of a** , 

or that a~^= — . 
a 

The Imaginary Quantity arises by a similar pi'ocess of gen- 
eralization. In the general expression ^a, n may be even 
and a may be negative, which gives us such expressions as 
"^-4,^ -8, V _16^ etc. Or, given general methods of solving 
quadratic equations, imaginar}'' expressions may arise from 
the solution of such equations, as x2 =— 4, or ^•2— 2a;=— 5. 
This expression must also be interpreted. In the same way, 
otlier ideas arise in algebra from the generality of the notation 
and of the methods used 

Division of Subject. — The science of algebra admits of 
the same fundamental divisions as arithmetic. These pro- 
cesses are all included under the three heads ; S^'-nthesis, Analy- 



TEACHIXG ALGEBRA. 4f>5 

sis, and Comparison. The fundamental operations arc Addi- 
tion, Subtraction, Multiplication, and Division. The deriva- 
tive or secondary processes are Composition, Factoring. 
Common Multiple, Common Divisor, Involution, and Evo- 
lution. Comparison gives rise to the Equation, Ratio, 
Proportion, the Progressions, etc. 

Each of these processes, on account of the generality of the 
symbols and operations, gives rise to processes and expres- 
sions not found in arithmetic. In respect to the new process 
called Composition, we remark that its scientific necessity is 
seen from the fact that each analytic process has its corre- 
sponding synthetic process. Thus addition is synthetic, 
subtraction is analytic, multiplication is synthetic, division is 
analytic, etc.; it follows, therefore, that there should be a syn- 
thetic process corresponding to the analytic pi'ocess of Fac- 
toring. This process we have called Composition; and its 
value is especiallj^ apparent in algebra, on account of the 
several interesting and practical cases which it embraces. 

The Equation. — The fundamental process of comparison 
in algebra is that of the Equation. The equation makes its 
appearance in 'arithmetic, but is not of sufficient distinctive 
importance to be regarded as a distinct part of the science. 
In algebra, however, it is of fundamental importance ; and 
gives the science its principal value. Indeed, so largely does 
it enter into the subject, that it would not be very far from 
tlie truth to say that algebra is the science of the equation. 

The principal use of the equation is to compare unknown 
quantities, variously involved, with known quantities, the 
object being to find the value of these unknown quantities. 
In the effort to disengage the unknown quantity from tlie 
known and find an expression for its value in known terms, 
we discover methods of procedure called the solution or reso- 
lution of the equation. The solution of the equation gives 
rise to several processes, among which are Transposition, 
Substitution, Completing the Square, etc. 



436 METHODS OF TEACHING. 

The solution of the general equation has never been deter- 
mined, and is no doubt impossible. The solution of the cubic 
and bi-quadratic is attended with difficulties that render the 
present methods not entirely satisfactory; and the solution of 
the general equation beyond the fourth degree has never been 
accomplished and is believed to be impossible. But though 
no solution of the general equation has been found, many pro- 
perties have been discovered that enable us to know much 
about their roots. These properties embrace some of the 
most beautiful things in the science of mathematics, such as 
Descartes' Rule, Sturm's Theorem, etc., and confer immor- 
tality upon their discoverers. Besides these, we have in 
Horner's Method a general metliod of solving all numerical 
equations that have real roots. 

Measoniuff. — The reasoning of algebra is essentially de- 
ductive. The comparison of quantities is usually that of 
equals, the relation being expressed by the equation. This 
equation is operated upon in various waj^s, all the operations 
being conti'olled by the axioms of the science. All the ope- 
rations of addition, subtraction, transposition, substitution, 
etc., are governed by axiomatic principles, and this makes the 
reasoning deductive. 

Induction, — Though algebra is a deductive science, it is 
possible to derive some of its truths by induction. Indeed, 
many of the first generalizations of its symbols are inductive 
in their character. Several of its leading truths were discov- 
ered by an inference from particular cases, and were after- 
wai'd demonstrated. Newton's Binomial Theorem was derived 
in this way ; and it is presented in this manner to the students 
of elementary algebra. The divisibility of a'>^ — b^ by a — b 
ma}' be inferred from the truth of the several cases a^ — 6^^ 
a^—b^^ a4_&4^ etc. 

3Iatheniatical Induction. — There is a method of reason- 
ing in algebra called mathematical induction^ which differs 
from pure induction. Mathematical induction derives a gen- 



TEACHING ALGEBRA. 437 

eral truth b}^ showing that what is true in n cases is true in 
?i+l cases ; while pure induction proceeds upon the principle 
that what is true in many cases is true in all. The principle of 
mathematical induction is used by many writers in proving 
that o" — b'^ is divisible by a — &, and also in giving a general 
demonstration to the Binomial Theorem. 

History of Algebra. — The first known treatise on algebra 
is found in the Arithmetic of Diophantus, written in the 
fourth century. Though not presenting a complete ti-eatise 
on algebra, it lays an excellent foundation for the science. It 
contains the first enunciation of the rule that " minus multi- 
plied by minus produces plus ;" solves such problems as 
"Find two numbers such that the sum or difference of their 
squares are squares;" and then proceeds to the solution of a 
peculiar class of problems which belong to what is now called 
indeterminate analysis. 

It is supposed that some of the principles were known be- 
fore the time of Diophantus ; but he greatly enriched the 
science with new applications. He shows great skill in the 
subject, presenting some elegant solutions, and is regai'dedas 
the author of Diophantine Analysis. The celebrated Hypatia 
composed a commentary on Diophantus, which is now lost. 
The work of Diophantus was discovered at Rome, in the 
Vatican library, about the middle of the sixteenth centur}'^, 
having probably been brought there from Greece when the 
Turks captured Constantinople. 

Algebra was introduced into Europe by the Arabs, who 
had carefully collected the writings of the Eastern mathemati- 
cians and written commentaries upon them. A copy of an 
Arabic original is preserved in the Bodleian Library at Oxford, 
bearing a date of transcript corresponding to the year 1342. 
This work is supposed to have been derived from the Hin- 
doos. Yery few additions to the science seem to have been 
made by the Arabs, though the}' cultivated it with great 
enthusiasm. The science of algebra was introduced into Italy 



438 METHODS OF TEACHING 

by Leonardo, a merchant of Pisa, who had travelled exten- 
sively in the East, in a work compose'd two centuries before 
the invention of printing. He could solve equations of the 
first and second degrees, and was particularly skillful in the 
diophantine analysis. Like the Arabian writers, his reason- 
ing was expressed in words at length, the use of symbols 
being a much later iuA^ention, 

The earliest printed book on algebra was composed by 
Lucas di Borgo, a Minorite friar. It was called Summa de 
Arithmetical Geonietria, Proportioni, et Proportionalita, and 
was published in 1494 and again in 1523. It followed Leon- 
ardo very closely ; but the mode of expression was very im- 
perfect, the symbols employed being a few abbreviations of 
the words or names which occurred in the process of calcula- 
tion, — a kind of short-hand arithmetic. The application was 
also limited, being confined to the solution of certain- problems 
about numbers. It included the solution of equations of the 
first and second degrees, the latter being divided into cases, 
each of which was solved by its own particular rule, man}' 
of which were derived from geometrical constructions, and 
expressed in Latin verses to be committed to memor3\ 

Up to the fifteenth century, the science was limited to the 
solution of equations of the first and second degrees. In 1505 
Scipio Ferreus, a professor of mathematics in Bononia, dis- 
covered the solution of a particular case of an equation of 
the third degree. Ferreus communicated his discovery to a 
favorite scholar, Florido, who challenged Tartaglia, a noted 
mathematician, to a trial of skill in solving questions. Tar- 
taglia had, however, discovered the solution of four cases of 
cubics, and came off" victorious. Cardan, Professor of Mathe- 
matics at Milan, made great efforts to obtain the rules of 
Tartaglia, who finally consented to show his method, which 
Cardan, in violation of an oath of secrecy exacted by Tartag- 
lia, published with some improvements, in a work he was 
then preparing. Lewis Ferrari, a pupil of Cardan, soon after- 



TEACHING ALGEBRA. 439 

wards discovered the solution of an equation of the fourth 
degree. In 1572, Bombelli, an Italian mathematician, pub- 
lished a work in which he explained the nature of the irre- 
ducible case of cubic equations, which had perplexed Cardan. 

In 1540 Recorde published his famous Wietntone of WMe, 
in which the sign of equality first appeared. Vieta (1540- 
1603) was the first to employ general charactei's to represent 
known quantities, which was a great step in advance. He 
also improved the theory of equations and gave the first 
method of solving them by appi'oximation. Albert Girard 
(1629), a Flemish mathematician, was the first to speak of 
Imaginary Quantities ; and inferred also by induction that 
any equation has as many roots as there ai'e units in the num- 
ber of its degree. Thomas Harriot made the important dis- 
coveiy that ever}'^ equation may be regarded as formed by the 
product of as many simple equations as there are units in the 
number expressing its oi'der. He also made several changes 
in the notation, and added several signs, so that as it came 
from his hands it differed very little from its form at the pres- 
ent time. Descartes (1637) made one of the greatest improve- 
ments by the application of algebra to curved lines, which 
resulted in a new branch, Analytical Geometry. 

The science was subsequently enriched by Newton, who dis- 
covered the binomial theorem, and b}^ Euler, who made exten- 
sive applications of it. Lagrange was the first to prove that 
eveiy numerical equation has a root, which had previously 
been only assumed. Gauss, 1801, developed the subject of 
binomial equations; W. G. Horner, in 1819, published his 
celebrated method of solving numerical equations ; and in 
1829 Sturm made known his beautiful theorem for assigning 
the position of the real roots of an equation. 

The latest improvement is the development of the subject 
of Determinants. The germ of this theory is found in the 
writings of Leibnitz. It was revived more than tift3f years 
afterwards by Cramer, and was extended by Gauss and others. 



440 METHODS OF TEACHING. 

It has received its latest and fullest development at the hands 
of two great English mathematicians, Cayley and Sylvester. 

Method of Teaching Algebra. 

We shall now give a brief discussion of the method of teach- 
ing algebra. We shall present several principles to guide the 
teacher in the instruction, then show how to teach some of the 
elementary portions of the subject, and then close the article 
with a few general suggestions to the teacher. 

Principles of Instruction, — There are several general prin- 
ciples which should guide the teacher in presenting the sub- 
ject of algebra to the beginner. 

1. We should lead the pupil to make the transition from 
arithmetic to algebra; algebra grew out of arithmetic. This 
is in accordance with the genesis of the science. It is also 
indicated by the law of thought from the particular to the 
general, algehra. being a kind of general arithmetic. We 
should introduce algebraic methods while teaching arith- 
metic. Mental ai'ithmetic, especially, may be made to flow 
natui'ally into mental algebra. Algebraic methods may also 
be introduced into written arithmetic, as in percentage, i= 
hr ; also in interest, as i=:ptr; and also in the progressions, 
etc. In advanced arithmetic, many of the subjects should be 
generalized and presented in algebraic notation. 

2. We should begin algebra ivith concrete problems, and not 
with the abstract operations of the science. This is also in 
accordance with the laws of thought. It is als<) the historic 
order; algebra was an outgrowth of the attempt to solve con- 
crete problems. It makes the siibject much easier for pupils, 
as they catch the spirit of the algebraic method, and are thus 
better prepared to understand the abstract operations of the 
science. The more recent writers on elementary algebra 
make a great mistake in omitting such exercises as an intro- 
duction to the subject. 

3. The pupil should have a thorough drill in the practice 



TEACHING ALGEBRA. 



441 



of algebra. Algebra is a calculus, and the pupil needs to be- 
come skillful in algebraic manipulations. It is discouraging 
to have pupils in analytical geometry and calculus, who are 
constantly making mistakes in the algebraic opei'ations. 
There should be a large collection of examples in the funda- 
mental rules, fractions, equations, radicals, etc., to afford the 
means of acquiring this skill. The teacher of elementar}' 
algebra should select and prepare two or three times the num- 
ber of examples found in any ordinary text-book on algebra, 
and drill his pupils on them. 

Course of Instruction. — The course of instruction in ele- 
mentary algebra should include the following things : 1. An 
Introduction, including the solution of concrete problems and 
the introduction of the algebraic S3'mbols ; 2. Algebraic No- 
tation ; 3. Explanation of the Negative Quantity ; 4. Funda- 
mental Operations ; 5. Secondary Operations ; 6. Fractions ; 
T. Simple Equations; 8. Solution of Problems, etc. 

1. lutrodHction. — To introduce the subject of algebra, 
take a simple problem in mental arithmetic, and write out 
the analysis upon the board, and then transform this anal}-- 
sis into the abbreviated method of algebra. To illustrate, take 
the problem, " William has 3 times as many apples as Henry, 
and both have 24; how many has each?" 
Illustration. — By arithmetic we solve the problem as follows : 

Henry^s nnmber, plus three times Henry's number, equals 24 ; 

Hence 4 times Henry's number equals 24 ; 

And once Henry's number ec^uals | of 24, or 6, etc. 

Now, if we represent the expression, " Henry's number," by some 

character, as the letter x, the solution will 

be made shorter, as seen in the margin. If ^ Pl^s 3 times a; equals 24; 

we now use 3.r to represent "3 times x," and ^^f^ ^ ^imes ,r equals 24; 

' ' and once x equals 6. 

Ax to represent ' ' 4 times x, the symbol =: 

for the word "equals," and the symbol -\- a;4-3a^=24; 

for the word "plus," the solution will be 4i;=24; 

cc — 6 
still shorter, as seen in the marghi. This 

solution is purely algebraic, and is a type 

of the entire nietliod of algebraic reasoning. 

19* 



442 METHODS OF TEACHING. 

The pupil will see that the last solution is the same as the 
J5i"st, except that we use characters instead of words. These 
characters are called symbols. The pupil may then be shown 
that 2x, 3x, etc., means " 2 times a;," " 3 times a?," etc.; that 
" one-half of .a;," " 2 thirds of a;," are expressed thus : ^a;, fa;, 

or— ^, • — , etc. He may also be told that an expression like 
2 3 

x-\-3x=24:, is called an equation. The pupil should then be 
drilled on the solution of concrete problems until he is familiar 
with the algebraic idea, and the fundamental principles of 
notation. Problems may be selected in which all the simple 
elements of notation may be gradually introduced. Symbols 
for known quantities may also be used. For classes of prob- 
lems, see author's Elementary Algebra. 

2. Algebraic N^otation.— The pupil is now ready for a for- 
mal explanation of algebraic notation. The various symbols 
should be presented, and the pupil quite thoroughly drilled in 
reading and writing algebraic exj^ressions. It will be well 
also to drill the pupil \i\ finding the numerical value of alge- 
braic expressions by substituting numbers for letters. 

3. Negative Quantity. — The next step is to explain the 
meaning and use of the negative quantity, as this will be 
needed in understanding the fundamental operations. We 
first show that a positive quantity mesms an additive quantity, 
and denotes that something is to be increased by it ; and that 
a negative quantity is a subtractive quantity, and denotes that 
something is to be diminished by it. We next lead the pupil 
to see that, since positive and negative are opjjosite in meaning^ 
they may be used to represent quantity considered in opposite 
directions or senses. Thus, if we use -f- to represent a per- 
son's gains in business, we may use — to represent his losses ; 
north latitude may be denoted by + and south latitude by — ; 
future time by -f- and past time hy — , etc. It will thus be 
seen that the symbols -f and — may indicate the nature of 
quantity, as well as the operations to be performed on it. 



TEACHING ALGEBRA. 443 

Principles. — We next establish some principles pertaining 
to the negative quantity. Thus, since $8 united with $5 yain 
and $5 loss leaves $8, we infer that uniting +5 and — 5 makes 
nothing^ or that uniting a positive and negative quantity of 
the same absolute valive amounts to nothing. We next show 
that in algebra a positive quantity is regarded as greater than 
a negative quantity, whatever their absolute value. Thus, if 
we unite 8 with +4, and also with — 6, the first result is 12, 
and the second 2, from which we infer that +4 is greater than 
— 6. Such a drill on the nature of positive and negative 
quantities is absolutely necessary in order to understand their 
use in algebraic addition and subtraction. 

4. Addition. — Addition is most conveniently treated under 
two cases: 1, To add similar quantities ; 2. To add dissimilar 
quantities. The first case embraces two sub-cases: 1. When 
the signs are alike; 2. When the signs are unlike. When the 
terms have the same sign, the process is entirely simple ; when 
they have unlike signs, the process needs explauation. 

Methods. — There are two methods of explaining this case, 
which we distinguish as the Old Method and the New Method. 
The New Method introduces the idea of an auxiliary quantity; 
that is, it assumes that a jiositive term, denotes that some 
quantity is increased by the term, and a negative term 
denotes that some quantity is diminished by the term. 

Illustration. — Prob. What is the sum of 7a and ia, or — 7a and — 4ffl? 
Sol. The sum of 7rt and 4a is evidently 11a ; and the sum of — 7a and — 4a 
is evidently — 11a, Prob. What is the sum of 7a and — 4a? Sol. Phis 
7a denotes some quantity increased by 7a, and — 4a denotes some quantity 
diminished by 4a ; and any quantity increased by 7a and diminished by 
4a, is evidently increased by 3a ; hence the sum of 7« and — 4a is -(-3a. 
Prob. What is the sum of — 7a and -}-4a ? Sul. A quantity diminisJied 
by 7a and increased by 4a is evidently diminislied by 3a ; hence the sum 
of — 7a and -l-4a is — 3a. We may also explain the sum of 7a. and — 4a 
as follows: 7a=3a-|-4a; and — 4a united with 4-4a is zero. Hence 
—4a united with 3a-f-4a equals -f-3a. 

.>. Subtraction. — Subtraction is convenient!}' presented 



444 METHODS OF TEACHIXQ. 

under two general cases : 1. When the terms are similar ; 2, 
When the terms are dissimihir. The former includes two sub- 
cases : 1. When the terms have like signs ; 2. When the terms 
have nnlike signs. The second principal case includes two 
sub-cases: 1. Monomials; 2. Polynomials. 

Ilethods. — There are several methods of explaining sub- 
traction, among which we may mention the following : 1. A 
new method ; 2. Leibnitz's method; 3. Adding to both terms; 
4. Negative quantity less than zero; 6. Latitude and longi- 
tude method. The new method makes use of the auxiliary 
quantity, regarding +2a as denoting some quantity increased 
by 2a, and — 3a as denoting some quantity diminished by 
— 3a; the '■'■some quantity'''' being used as auxiliary in the 
process. 

Illustration. New Method. — Pkob. Subtract la from 4rtt. Sol. A 
quantity increased by 4^6 is evidently 3rt less than the quantity increased 
by 7rt ; hence 4/? minus la equals — 3a. In a similar manner we may 
explain the following problems: (2). — la minus —4a ; (3). — 4<x minus 
— la; (4). — la minus 4a; (5). la minus — 4« ; (6). 4« minus — la; 
(7). — 4'i minus 7a. Prob. Subtract — c from a. Sol. The difference 
between a quantity increased by a and diminished by c is evidently the 
sum of a and c, or a-\-c ; hence — c subtracted from a equals a-\-c. 

The Method of Leibnitz would solve the last problem thus: a=a+c — c, 
and —c subtracte4 from a+c — c equals a+c. This cannot be applied 
conveniently to the problems given above. The method of adding to 
both terms is as follows : adding c to a, we have a^c ; adding c to — c 
we have c— c=0 ; and subtracted from a-\-c leaves a+c ; hence, since 
the difference between two quantities equals the difference between the two 
quantities equally increased, — c subtracted from a leaves a-[-c. By the 
method of Latitude and Longitude, we consider la as representing so 
many degrees north of the equator, and — ia as representing so many 
degrees south of the equator; and the difference between la nordi and 
4a south is evidently 7a+4a, or 11a. It is not so convenient in this 
method, however, to fix the sign of the difference. The general case 
may be explained by subtracting b—c from a. 

6. Multi2)licatiou. — Multiplication is conveniently treated 
under two cases: 1. To multipl}^ by a monomial; 2. To multi- 



I 



TEACHING ALGEBRA. 445 

ply by a polynomial. In presenting multiplication, there are 
four things which require attention: 1. The Co-efficients; 2. 
The Literal Part ; 3. The Exponents ; 4. The Signs. To ex- 
plain the multiplication of the co-efficient and the literal part, 
let the pupil see clearly the principle, Multiplying any factor 
of a quantiiy multiplies the quantity. To explain the expo- 
nents, show that, The exponent of a term in the product 
equals the sum of its exponents in the factors. 

Ifethods. — There are two methods of explaining the signs, 
called the Monomial Method, and the Binomial Method. The 
Binomial Method explains by multiplying a — b by c — d; and 
has usually been emplo^^ed by mathematicians. The Mono- 
mial Method is preferable, however, as it looks the difficulty 
squarely in the face, and shows just why the signs should be 
as they are. 

Illustration. — To determine the law of the signs, we will multiply h 
hy a ; —b hj a ; 6 by — a ; and — b by — a. 

First, +^ taken any number of times, operation. 

as a times, is evidently -\-nb. +" b -\-b —b 

Second, —b taken once is— &; taken 



twice, is —2b,etc.; hence, -Z>, taken any +"^ """* "^'^ =+«? 
number of times, as a times, is —ab. 

Third, b multiplied by — a, means that b is to be taken sxbiractively a 
times; b taken a times is ab, and taken subtracticely is —ab. 

Fourth, — b multiplied by — «, means that —b is to be taken subtract 
ively a times ; —b taken a times is — ab, and used subtractively is — ( — aJ>), 
which, by the principles of subtraction, is -\-ab. 

Hence, we infer that the product of quantities Jiaving like sirpis is plus, 
and having unlike signs is minus. 

%. Division,. — Division is conveniently ti'cated under two 
cases: 1. To divide by a monomial; 2. To divide by a poly- 
nomial. There are four things to be considered, as in multi- 
plication: 1. The Co-efficients; 2. The Literal Part; 3. The 
Exponents; 4. The Signs. The explanation of the division 
of the co-efficients and letters depends on the principle, 
Taking a factor out of a quantity divides the quantity by that 
factor. The explanation of the exponents depends on the 



446 METHODS OF TEACHING. 

principle, The exponent of a term in the quotient equals its 
exponent in the dividend minus its exponent in the divisor. 
The law of the sio-ns is derived from the law of the sifjns in 
multiiDlication. 

8. Composition and Factoring. — For the ti'eatment of 
Composition and Factoring, see the anthor's Elementary 
Algebra. Attention is called especially to the demonstration 
of the theorem concerning the divisibility of a** — h"^ hy a — 6, 
and theorems similar to it. The usual method is that of mathe- 
matical induction ; the method we have given is much simpler. 
It is suggested chat the student be thoroughly drilled in Fac- 
toring, as it lies at the basis of algebraic analysis. The 
student-teacher may be required to give an outline of the 
several cases, and show how to teach them. 

'9. Fractions. — Fractions, in algebra, are to be regarded as 
the expression of one quantit}^ divided by another. The 
principles are established by demonstration, and then are to 
be applied in deriving the rules of operation. Let the student- 
teacher give an outline of the cases, and explain the method 
of their treatment. Show also what difficulties pupils usually 
meet with, and how to explain them. 

10. Equations. — The elements of equations are simple and 
readil_y taught. Some teachers illustrate transposition by a 
jmir of scales or balances, showing that if anything is put 
into or taken from one scale an equal quantity must be put 
into or taken from the other scale. Such an illusti'ation is 
not needed, however, as a pupil i-eadily grasps the axiom that 
if equals be added to or taken from equals, the results will be 
equal. The pupils should be thoroughly drilled on the solu- 
tion of equations until they are ftimiliar with the general 
methods and all the special artifices that apply to particular 
cases. 

11. Solution of Froblenis. — Pupils should have an extensive 
drill on the solution of concrete problems. The solution of 
such problems consists of two parts; the forming of the 



TEACHING ALGEBRA. 447 

equation, and the solution of the equation. The first is called 
the concrete part, the latter the abstract part of the solution. 
The pupil should have wide and extensive experience in both 
of these, for it is only in this way that he can become a skill- 
ful algebraist. He may also be encouraged to make new 
problems for himself and schoolmates to solve. 

General Suggestions. — We close the subject with some 
general suggestions to the teacher. . 

Lit-eral Notation. — The teacher should be careful to see 
that the pupils have a clear idea of the literal notation. First, 
they should see clearly that a letter represents a general num- 
ber, and that this number may be integral or fractional. 
Second, that as involved in an expression, each letter is a 
factor. There should be a drill with figures, as 3x4x5, and 
then changing to axbxc, and then to abc^ until this idea is 
clearly developed. 

Positive and Negative. — The pupil should be led to a clear 
idea of the positive and negative quantities. He should first 
be taught that + and — denote operations. He should next 
see that the}' give character to quantities, and indicate posi- 
tive and negative quantities. He should then be led to under- 
stand that they may be used to represent quantities reckoned 
in opposite directions. 

Exponentfi. — The pupil should first learn to use and under- 
stand exponents as indicating the powers of quantities. After 
he has i-eached the idea of generalization in algebra, he should 
see that in a'^ , the n being general iraxy be integral or frac- 
tional, and that when fractional the numerator denotes a 
power, and the denominator a root. Again, since n is general 
it may be negative^ and as such needs an interpretation, the 
origin and meaning of which should be clearly shown. And, 
again, ?i being general, a" maybe a^ or a", each of which 
should be clearly interpreted. The use of fractional exponents 
in radicals should be thoroughly understood, and the pupil, 
should be taught to work radicals largely through fractional 



448 METHODS OF TEACHING. 

exponents. This will simplify many points that are, at first, 
quite difficult for the learner. 

Generalization. — The pupil should be thoroughly drilled 
in the generalizations of the science. The spirit of generali- 
zation lies at the basis of algebra, and no one can understand 
it until he is thoroughly imbued with this spirit. Pupils 
should be required to generalize special problems and derive 
a general rule. They should discuss these general expres- 
sions, show the cases that may arise for different suppositions, 
and apply these expressions in the solution of problems of a 
given class. 

Interpretation. — The pupil should be trained to interpret 
algebraic results. The solution of the general simple equa- 
tion^ax — &j;=c, Vae problem of the couriers^ etc., should be 
discussed, and the different results which arise be interpreted 
The discussion of the roots of the general quadratic equation, 
a:;^-\-2px=q, showing the relations of p and q to the roots, is 
a most valuable exercise, and tends to imbue the mind of the 
pupil with the true algebraic spirit. No one is an algebraist 
who cannot interpret results ; and a knowledge of its applies^ 
tion to the physical sciences is impossible without the ability 
to discuss and interpret general formulas. 



PHYSICAL SCIENCE 



CHAPTER I. 



NATURE OF PHYSICAL SCIENCE. 

THE Phy.sical Sciences are the sciences which treat of the 
material world. They consist of facts and phenomena, 
and the truths and principles which relate to them. They 
begin in the observation of facts, these facts are classified, 
and the causes which produce them and laws which control 
them are ascertained. 

The object of these sciences is the interpretation of the 
physical universe. They assume that man is the interpreter 
of nature, and that science is its right interpretation. They 
are based on the uniformity of nature, and thus give foresight 
to man and enable him to predict what will take place in the 
future. The scientist thus makes ^^remsion, or the prophetic 
nature of knowledge, the basis and test of science. Reason- 
ing from the standpoint of the physical sciences, Herbert 
Spencer defines all science as merely the power of prevision. 

I. Classification. — No complete classification of the phys- 
ical sciences has yet been given which is satisfactor3\ They 
so overlap and interlace that it is difficult to draw a clearly 
marked line of distinction between them. The pi'incipal 
branches are Natural Histor}', Natural Philosophy, Astrono- 
my, Chemistry, Geography, Geologj'^, Biology, etc. These 
branches are distinguished partly by their subject matter and 
partly by their objects and methods of development. 

(441)) 



450 METHODS OF TEACHING, 



^ 



Natural History. — Natural History treats of the three 
kingdoms of nature, — the mineral, the vegetable, and the 
animal kingdoms. Its olyect is to ascertain the facts relating 
to the nature, structure, and growth of the individual objects, 
and to arrange these objects in scientific classes. It assumes 
that they were created after great pattern ideas, and that the 
object is to discover these ideas in their development, and to 
classify accordingly. They have been appropriately called 
the Classificatory Sciences. The grand object of Natural 
History, therefore, is classification. 

The branches of Natural History are Zoology, Botany, and 
Mineralogy. In Zoology it is assumed that the animal king- 
dom was created after four great leading ideas or types of 
structure, called Yertebrates, Articulates, Radiates, and 
Mollusks ; and that these ideas are differentiated all the way 
down to species and individuals. In Batany two great lead- 
ing types are found, the Phisnogamia and Cryptogamia, each 
of which constantly divides into subdivisions, ending at last 
in species and individuals. Mineralogy is also regarded as 
the development of ideas which form distinctly marked 
classes. 

Natural Philosophy. — Natural Philosophy treats of the 
facts and phenomena of the material world. Its object is to 
ascertain these facts and phenomena, and to discover the 
causes which produce them and the laws which govern them. 
Thus, in respect to falling bodies, it ascertains the cause to be 
gravity, and the law that the distances are proportioned to the 
squares of the times. It seeks to acquire the facts respecting 
Light, to explain these fticts by the cause of undulatory 
motions, and to discover the laws of reflection, refraction, etc. 
It differs from Natural History in that its facts do not admit 
of classification into genera and species; and also in that it 
deals more particularly with laws and causes. 

The principal branches of Natural Philosophy arc Mechan- 
ics, Hydrostatics, Pneumatics, Optics, Acoustics, Thermotics, 



NATURE OF PHYSICAL SCIENCE. 451 

etc. Mechanics treats of the general laws of force ; Hydro- 
statics treats of liquids; Pneumatics treats of the air; Optics 
treats of light; Acoustics treats of sound; Thermotics treats 
of heat; etc. These divisions seem quite distinctly marked, 
and yet there are indications of future changes; and. even the 
term Natural Philosophy may not be always used to include 
the several branches above named. 

Astronomy. — Astronomy treats of the facts and truths re- 
lating to the heavenly bodies. It is closely related to Natural 
Philosophy, differing mainly in the subject matter of its in- 
vestigations. It explains the appearances, changes, motions, 
etc., of the heavenly bodies, calculates their size and distance, 
investigates their composition, structure, etc. It is appropri- 
ately named the " sublime science," and gives us the grandest 
ideas of the nature and magnitude of the physical universe. 

Chemistry. — Chemistry treats of the nature and properties 
of the elements of bodies. It differs from Natural Philos- 
ophy in that the former considers the general laws of matter 
in the forms in which it presents itself, while Chemistry con- 
siders the elements out of which matter is composed, and ex- 
plains the changes that occur in bodies through .the operation 
of these elements. Its object is to ascertain the composition 
of material tilings, and to explain the method of their forma- 
tion. It regards matter as composed of infiniteh^ small ele- 
ments called atoms; and thus occupies about the same place 
among the physical sciences that the infinitesimal calculus 
does in the mathematical sciences. 

Biology. — Biology is the science which treats of life, or 
living matter. It seeks to ascertain the facts and understand 
the laws of the life principle found in matter, and endeavors 
to explain the complicated phenomena of living beings. It 
rises above the other natural sciences in tliat it treats not only 
of matter, but of organized matter; it considers not merely 
force, but that life force which holds matter in its hand, and 
shapes it into the organic beings of the vegetable and animal 



452 METHODS OF TEACHING. 

world. It is a science of recent development; and though 
difficult, and still in an incomplete condition, is one of great 
interest, and promises to be of great practical value. There 
are several other branches of the Physical Sciences, as Geol- 
ogy, Geograph}^, etc. 

II. Elements op Physical Science. — The several elements 
of the Physical Sciences are Facts and Phenomena, S,ystems 
of Classification, Causes of Facts and Phenomena, Laws 
governing Facts and Phenomena, and Truths growing out of 
them. The object of the inquirer in these sciences is to at- 
tain these elements. 

Facts and Phenomena — The primary elements of the 
Physical Sciences are Facts and Phenomena. A Fact is 
something that is or has been. It is a particular truth in the 
domain of sense. It is something seen or heard, or that was 
revealed through one of the senses. It is confined to the 
present or the past, and does not reach out to the future, as 
that is the sphere of a truth. Thus jt is a fact that "the sun 
rose this morning," that "there was snow last winter," that 
"water will freeze at 32° above zero," etc. A Phenomenon is 
literally an appeai-ance ; as the twinkling of a star, the chang- 
ing of the moon, the rising of the tide, etc. The statement 
of a phenomenon in a proposition gives us a fact. 

Classifications. — Several of the Physical Sciences aim 
especialh^ at the classification of facts. In Natural History"- 
the principal elements are fticts and their classification. In 
these sciences it is assumed that the world was constructed 
after great pattern ideas or plans of structure; and objects 
are classed by means of these ideas. Zoology embraces all 
the animals under five great divisions; Branches, Classes, 
Orders, Families, Genera, and Species. The Branches repre- 
sent the plan of structure; the Classes, the manner of execu- 
tion; the Orders, the comparative complication of execution; 
the Families, ditferences of form ; Genera, details of structure ; 
Species, difference in size, habits, etc. The great divisions in 



NATURE OF PHYSICAL SCIKXCE, 453 

Botan)'^ are Species, Genera, Orders, Cohorts, Classes, and 
Sub-kinffdoras; divisions founded in nature, and tlius called 
the Natural System. 

Causes. — The grand aim of the Physical Sciences is to 
ascertain the Causes of things. By a Cause is meant that 
which produces an event, or but for which some event would 
not occur. The great question of Physics is why ; and the 
answer to this question gives us a large body of scientific 
truths. Thus, gravity explains why a stone falls, and also 
the planetary motions ; the earth revolving on its axis ex- 
plains the phenomena of day and night ; elliptical orbits with 
the sun in a focus explain the changes of the heavenly bodies; 
the undulations of an ethereal fluid explain the interesting 
phenomena of light, etc. These causes are reached through 
hypothesis and theory. 

Latvs. — The second great aim of the Phj'sical Sciences is 
to ascertain the Laws of ph3^sical phenomena. By Laws we 
mean the regular mode or order according to which something- 
operates or events take place. This element is closely related 
to the inquiry for the Cause, but yet is different from it. Thus, 
gravity is the cause of a body falling, but it is a law that the 
force of gravity varies inversely as the square of the distance, 
or that the distances passed over by a falling body are in pro- 
portion to the squares of the times. The cause of the changes 
of the planetary bodies is an elliptical orbit; and a law of mo- 
tion in such an orbit is that the radius vector passes over 
equal areas in equal times. 

Truths. — A Truth of physical science is a statement of 
some established principle, or some inference derived from it. 
Truths embrace both laws and causes, the statement of a law 
or a cause being a truth. The statement of any general pro- 
position which has been verified, or any inference derived from 
it, is also a truth. Thus, heat expands all metals, or there 
will be a total eclipse of the sun daring such a year, are also 
truths. The truths of physical science are mainly derived by- 
inductive reasoning, and enable u.-; to pri'dict the-future. 



454 METHODS OF TEACHIXG. 

III. How Developed. — The Ph3"sical Sciences begin in the 
common observations of mankind. This common knowledge 
is, b}^ the power of thought, gradually transformed into scien- 
tific knowledge. Through the operation of the natural laws 
of mental activity, the common knowledge of the race is con- 
stantly rising up into the higher aud more perfect forms of 
science. The several elements that enter into their develop- 
ment are Observation and Experiment, Classification, Induc- 
tion, Deduction, Hypothesis, and Theor3^ 

Observation. — Observation has reference to the perception 
of nature as she presents herself to our view. By it facts 
and phenomena are presented to the mind through the senses, 
and are then retained in the memory for future use. In sci- 
ence, this observation needs to be careful and exact; mere 
looking or listening is not sufficient, we must look and listen 
with the eye of reason. Observation mast be made with 
patience, and sources of error must be guarded against. It 
must also be analytic; facts and phenomena must beanah'zed, 
things must be separated or broken up into fragments in order 
that the information may be minute and accurate. Man also 
invents instruments, as the microscope and telescope, to aid 
the senses in observation, and thus acquire facts which he 
could not otherwise obtain. 

E.vperinient. — B}^ Experiment, man puts nature into new 
relations to observe the results. He not only observes, but 
he prepares his facts for observation. Objects are placed in 
different relations and conditions, and the changes and results 
noted and compared. Nature is, as it were, put on the wit- 
ness stand, and, by a series of cross questions, forced to reveal 
her secrets. This method of obtaining facts is largely used 
in Natural Philosophy, and in Chemistr3Mt is in constant use. 

Classification. — As facts multiply, the mind compares them 
and perceives points of resemblance between them, and forms 
them into classes. The perception of the similarities and dif- 
ferences is an act of Judgment ; the separating of the common 



NATURE OF PHYSICAL SCIEN-CE, 455 

qualities to unite them into a general scheme is abdractio7i, 
and the forming of the general class idea is generalization. 
The arrangement of the objects themselves into classes is 
called clanHificaiion. This process of classification is neces- 
sary in all the sciences; but it is especially prominent in 
Natural Ilistor^'. 

Induction. — Induction lies at the basis of the truths of 
the Physical Sciences. Observation and Experiment give 
us the particular facts ; Induction takes these facts and finds 
the laws which contain or control them. Thus from the facts 
that heat expands iron, zinc, copper, etc., we derive by In- 
duction the general truth that heat expands all metals. It is 
this process of thought, so generally neglected by the an- 
cients, and made so prominent in the Baconian system, that 
has given such rapid growth to the physical sciences during 
the last century. 

Deduction. — The method of Deductive reasoning is also 
used in the Physical Sciences. Having reached a general 
conclusion by Induction, we apply this truth to new facts by 
a process of Deduction. Thus, if we discover a new metal, 
we immediatel3' infer that heat will expand it, from the gen- 
eral principle that heat will expand all metals. The mathe- 
matician takes the doctrine of universal gravitation, puts it 
into an equation, and works out, in the solitude of his study, 
the position o-f a new planet ; and the telescope, sweeping the 
field of the heavens, discovers the wanderer, and thus confirms 
" the immortal predictions of science." It is thus true that 
" Induction discovers principles, while Deduction applies 
them ;" or as T^'udall observes, " In the study of Ph3'sics, in- 
duction and deduction are perpetually married to each other." 

Hf/pothesis. — The Physical Sciences are aided in their 
development b}' Hypothesis. An Hypothesis is a supposition 
to account for facts and phenomena. The facts are presented 
through the senses, and the mind makes some supposition to 
account for them. Such suppositions, or hypotheses, have 



4:56 METHODS OF TEACHING. 

given us a large number of the truths of the phj'sical scien- 
ces. Nearly all their great truths were once hypotheses. Kep- 
ler's law of elliptical orbits was once a mere hypothesis ; he 
made and rejected nineteen before he discovered the true one. 
Newton's theory of gravitation was at first only an hypothe- 
sis ; and when verified became an accepted truth. 

Verification — Having formed our hypothesis, the next step 
is to prove it to be true. This is called its verification. To 
verify an h^ypothesis, it must be shown that it will account 
for all the known facts to which it relates. If facts are found 
that it will not account for, another supposition must be made, 
and so on until one is obtained that is correct. Great care, 
however, must be taken, not to accept an hypothesis as true 
until the facts are so numerous that there can be no doubt of 
its verification. " To try wrong guesses." says Dr. Whewell, 
"is, with most persons, the only way to hit upon right ones." 

Origin of Hypotheses. — The hypotheses of science origin- 
ate by what is called anticipation. Anticipation is the pre- 
'saging of a truth before there is evidence to prove it. B}' the 
power of anticipation the mind leaps from a few facts to the 
law which governs them. All h^'potheses are the result of 
what La Place calls a "great guess," or of what Plato so 
beautifully designates as "a sacred suspicion of truth." The 
forming of hypotheses requires a suggestive mind, a lively 
fancy, a philosophic imagination, that catches a glimpse of the 
idea through the form, or sees the law standing behind the 
fact. 

Theory. — The Physical Sciences are largely made up of 
Theories. A Theory is an accepted explanation of facts and 
phenomena. It may also be defined as a verified hypothesis. 
When an hypothesis is shown to explain all the facts that are 
known, these facts being varied and extensive, it is said to be 
verified, and becomes a theory. Thus we have the theory of 
universal gravitation, the Copernican theory of the solar 
system, the undulatory theory of light, etc., all of which 
were originally mere hypotheses. 



NATURE OF PHYSICAL SCIENCE. 457 

IV. Yalue of Piiystcs. — The importance of the stud}- of 
the physienl sciences has, until recently, been hirg-ely over- 
looked in onr systems of education. Language, mathematics, 
and the metaphysical sciences, were, for many years, the prin- 
cipal branches of a collegiate and academic course. It is but 
recently that the physical sciences have, to any large extent, 
been introduced into the curricula of our higher institutions; 
and in our common schools they are still almost entirely 
omitted. A few remarks are therefore appropriate concerning 
the value of these studies. 

1. The atudy of the phi/.'^ical sciences gives culture to the 
perceptive powers. The physical sciences begin in the ob- 
servation of the facts of the external world. The proper 
study of these sciences requires the pupil to observe these 
facts closely and accurately. They thus call the perceptive 
powers into constant and forcible activity ; quicken and 
strengthen the power of the senses, and make the student 
sharp-eyed and accurate in his observation of things. Among 
all the studies, they especially, and almost alone, give culture 
to the perceptive powers. 

2. The study of the p)hysical sciences gives culture to the 
power of classification. The facts of the material world are 
created in classes, and the natural sciences embrace the classi- 
fication of the facts, as well as the facts themselves. These 
classifications, in several of the branches, are the most perfect 
tliat can be found in science. The arrangement into species, 
genera, orders, and kingdoms, as in botany, zoology, etc., has 
no counterpart in the other sciences. The natural sciences, 
therefore, transcend all others in atibrding cultivation to 
generalization and classification. They, above all other sci- 
ences, tend to train the mind to the habit of the s^'stematic 
and orderly arrangement of knowledge. 

8. The study of the physical sciences cultivates the power 
of inductive reasoning. All the primary ti'uths of these sci- 
ences are derived b}^ induction. In their stud}' we are con- 
20 



4oS 



METHODS OF TEACHINQ. 



stautly passing from particular facts to the general laws of 
which they are examples. In no other sciences is the use of 
induction anything like so prominent. Though some of these 
sciences may rise into a deductive stage, yet the entire spirit 
of these branches is inductive. Induction is the genius 
which presides over their origin and development. The mind 
of the student is thus constantly occupied in inferring general 
laws from particular facts, and acquires the hal)it of reasoning 
in this way. The importance of such culture is seen in the 
fact that this is the kind of reasoning that we use in the ques- 
tions that meet us in the ordinary duties of life. 

4. The study of the physical sciences tends to modify the 
dogmatic spirit cultivated by the deductive sciences. The 
study of the deductive sciences tends to make the mind over- 
bearing and dogmatic. The pure mathematician is as stub- 
born as a mule, in his belief. Accustomed to see certain con- 
clusions flow from admitted premises, he applies the same 
method to social and political questions, and is intolerant of 
any opposition to his opinions. N^atural science, leading the 
mind b}^ the path of inductive thought, accustoms it to see 
ho.w easy it is to be mistaken in an inference, and makes it 
cautious in its conclusions, and tolerant of doubt. The sci- 
entists are the most modest and the least positive in their be- 
liefs of any class of thinkers; indeed, many of tlie points of 
difference between theology and science are the inferences of 
the theologians from the premises of science, rather than the 
claims of the scientists themselves. The fact that the path- 
way of the physical sciences is strewn with the remains of 
discarded theories, is sufficient to cultivate a spirit of mod- 
estly and charity. 

5. The physical sciences have contributed to the development 
of the material interests of mankind. They have done much 
to lift man up out of a condition of barbarism and ignorance. 
They have enabled him to improve the tillage of the soil, to 
raise larger and better crops, to lessen and lighten his labor, 



I 



NATURE OF PHYSICAL SCIENCE. 459 

to establish manufactories, and in a thousand waj'S have min- 
istered to his comfort and convenience. The}^ have given him 
machiner}^ bv which lie can multiply his strength and skill, 
and do that which his unaided powers could never accomplish. 
They have built his houses, covered the ocean with the white 
wings of commerce, laid rails to carry his products across 
wide continents, disseminated education b}^ the invention of 
the printing press, and, b}' improving his material condition, 
enabled him to lift himself up into a higher civilization. 

Objections. — Though the physical sciences'are thus valuable 
to man, there are objections to the exclusive study of these 
branches. The natural tendency of such study is to lead to 
materialism in thought and philosophy. Accustoming the 
mind to the concrete, they unfit it to comprehend and appre- 
ciate abstract truth. They thus tend to lower the tone of 
man's thought and sentiment, to destro}^ the imaginative and 
poetic in literature, to take the divine element of inspiration 
out of art, and to weaken the religious faith of mankind. 
Though the sciences of geology and astronomy give grand 
ideas of the creation, and some of the other branches afford 
evidences of a marvelous design in organic life; and though 
some scientists have said that "the facts of the world are the 
thoughts of God," yet it must be admitted that the exclusive 
study of the physical sciences leads the mind naturally to- 
wards a hard, dry materialism, which has no place for the 
highest aspirations of the human heart, for God, Immortality, 
and Heaven. 



CHAPTER II. 



TEACHING GEOGRAPHY. 



GEOGrRAPHY treats of the facts relating to the surface of 
the earth. It seeks to describe and classify these facts, 
and to explain their causes and the laws which control them. 
The term Geography is derived from ye, the earth, and 
grapho, I describe, and means literally a description of the 
earth, and this was its primary sense. 

I. jSTature op GrEOGRAPHY. — Geography is not so much a 
distinct science as a collection of fticts and principles drawn 
from the other sciences. In its widest sense. Geography em- 
braces all that we know of the earth ; its form, size, motions, 
structure, present and past condition, products, inhabitants, 
etc. As usually treated, it runs into and embraces parts of 
several of the sciences, as astronomy, botauy, zoology, etc., 
though it has a sphere of its own somewhat distinct from any 
of these other branches. 

Division. — The most natural division of Geography seems 
to be into Physical and Political Geography. Physical Geog- 
raphy is that which pertains to the earth in its natural condi- 
tion, including land, water, the atmosphere, the climate, and 
the distribution of the mineral, vegetable, and animal king- 
doms. Political Geography is that which treats of the earth 
as modified by man, — its countries, cities, towns, and inhabit- 
ants, including their customs, religion, government, etc. 
Popularly, however, the term Physical Geography has been 
used to include the i)hilosophy of geography, embracing the 
generalizations of the science and a discussion of the causes 
and laws of geographical phenomena. 

Besides these divisions, writers speak of Local Geography, 
(4G0) 



TEACPIING GEOGRAPnY. 401 

Descriptive Geographj', Mathematical Geography., Historical 
Geography, etc. All of these have a special meaning, and are 
convenient in instruction, though they do not indicate scien- 
tific divisions of the subject. The division which comes near- 
est the present actual usage is that into Descriptive and 
Physical Geography; the former treating of the facts of geog- 
raphy, and the latter of the laws and causes of geographical 
facts. 

Orif/in. — Geography is a comparatively modern science. 
The geographical knowledge of the ancient Egyptians and 
Phoenicians was confined to the shores of the Mediterranean 
Sea. " The military expeditions of Alexander, in the fourth 
century B. C, extended the knowledge of the Greeks consid- 
erabl3\ Eratosthenes, about 200 B. C, first reduced the 
geographical knowledge of the Greeks to a scientifi^c form. 
Strabo and Ptolem}^ wrote treatises upon the subject, which 
contained nearly all that was known by mantind for several 
centuries. Prince Henry of Portugal, called the Navigator, 
added considerably to this knowledge during the fifteenth 
century. The discoveries of Columbus, however, opened up 
a new world and gave a new impetus to the discovery of 
geographical fiicts. The geographical societies of Prance and 
England have contributed largely to geographical knowledge 
during the last S'O or 60 years. 

The first text-book on geography published in this country 
was a small 18mo. manual b}' Jedediah Morse, issued in 1784. 
This was the principal text-book until 1822, when William C. 
Woodbridge and Mrs. Emma Willard issued a work entitled 
The Woodbridge and Willard Geographies and Atlases. In 
1823, Sidney E. Morse published a work entitled a New Sys- 
tem of Modern Geography^ which was several times revised 
and had a wide and long continued circulation. Some of the 
principal writers who followed Morse were Olney, Smith, and 
Mitchell, the works of the latter author being especially pop- 
ular. 



462 METHODS OF TBAGIIING. 

The earliest text-books made local geography very promi- 
nent, some works containing ver}^ little description. In in- 
struction, also, the description of geographical facts was gener- 
ally neglected. By degrees the descriptive part became more 
prominent, both in text-books and in instruction. The next 
step in advance was the attempt to classify the facts of geog- 
raph}^, and to present their laws and causes. The labors of 
Humboldt and Ritter in this respect were introduced into 
this country by Guyot in his lectures, and in a work entitled 
The Earth and Man. Several works were soon prepared on 
Physical Geography, in which the facts were classified into 
systems and their causes and laws explained. Recently at- 
temj)ts have been made to combine this with the local and 
descriptive geograph}' in text-books for j^oung pupils ; but not 
with entire success. One or two series that claimed such a 
combination as an especial merit, were found not to work well 
in the class-room, and had to be revised and made to conform 
more to the idea of presenting the facts of the subject before 
its philosophy. 

II. Methods op Teaching Geography. — There are two dis- 
tinct Methods of Teaching Geography, which are appropriately 
distinguished as the Analytic and Synthetic methods. The 
analytic method begins with the world as a whole and passes 
by successive division down to the state, county, and town or 
city, in which one resides. The synthetic method begins at 
the smaller division and passes by successive enlargements to 
the entire surface Of the earth. There is also the Inductive 
Method which begins with particular facts and passes to their 
generalization and laws ; and tlie Deductive Method which 
begins with a general view of geographical facts and passes to 
particulars. Some German writers speak also of the Con- 
structive Method ; but this seems to be a mere appendage to 
the other methods, and not a distinct method of itself. 

Synthetic 3Iethod The Synthetic Method begins at home 

and passes by successive additions over the whole globe. It 



TEACHIXG GEOGRAPHY. 463 

starts with the school-honse and yard, takes in the surround- 
ing farms, then passes to the township, the county, and the 
state, from the state to the United States and the Western 
Hemisphere, and at last covers the entire globe. 

Several reasons can be given in favor of the synthetic 
method. First, it seems to be more in accordance with the 
principle, from the known to the unknown, as it passes from 
the familiar things around us that we can see, to those that are 
distant and can only be conceived. Second, the pupil thus 
Hrst gains a knowledge of the geography of his own county 
and state, which it would seem is of more importance to him 
than a knowledge of remote countries of which he seldom 
hears or reads. The second consideration is especially im- 
portant if the time for the stud}'' is restricted or accident- 
ally curtailed, since the remote parts of the globe would thus 
be omitted rather than those with which his life will be most 
closel}'^ connected. An objection to the method is that the 
attempt to carry it out strictl}' and completely would make 
the course very tedious or lead to tiresome repetitions. A 
further objection is that the mind generally prefers to operate 
analytically, passing fronj a general view of the whole to a 
detailed consideration of its parts. 

Analytic 3Iethod. — The Analytic Method begins with the 
globe as a wliole and by successive divisions passes to the 
various parts of which it is composed. It divides the earth 
into land and water, comes down from the continents to the 
countries, states, counties, and townships, and from the large 
bodies of water to the smaller ones. This method is the reverse 
of the synthetic method, beginning whei'C that ends, and end- 
ing where that begins. 

Thei*e are several reasons in favor of the analytic method. 
First, it admits the early introduction of the globe. It thus 
gives a more correct idea of the relations and comparative 
size of the different countries, and prevents some of the 
wrong conceptions that inevitably flow from the other 



464 METHODS OF TEACHIXG. 

method. Second, it enables us to present earlier the astro- 
nomical elements of geography ; such as the changes of day 
and night, the changes of the seasons, the nature and the use 
of latitude and longitude, etc. Third, it follows the general 
law of acquisition, — from the whole to its parts, or from the 
larger part to the smaller part, instead of from details to the 
"whole. 

Inductive Method The Inductive Method begins with 

the particular facts of the science and passes to their classifi- 
cation into systems. It is in spirit the method by which the 
subject has been taught for many years, although until re- 
centl^^ the course did not pass beyond the facts of the subject. 
It is the manner in which it is now presented by those authoi'S 
who follow their work in descripti^'e geography by a work on 
Physical Geographj'. To carry out the method fully, we 
should begin with the facts of geography around us that we 
can perceive before we learn to define or describe them. 

Several reasons can be given in favor of the Inductive 
Method of teaching geography. It corresponds with the 
primary law of mental development, from the particular to 
the general. The mind naturally learns ftcts before it learns 
to classif}^ them into general systems. It is thus much easier 
than the deductive method, wdiich requires the grasp of a gen- 
eral system before the mind is familiar with details. 

Deductive 3Iethod. — The Deductive Metho^l of teaching 
geograph}^ begins with a general view of the facts, and ])asses 
to the particulars -embraced in the general system. It seizes 
xipon the laws or general characteristics of a group of facts, 
and interprets the particular facts from the conception of the 
group. Thus, from river systems it passes to particular rivers, 
from mountain systems to individual mountains, from facts 
that stand in the relations of cause to the effects which they 
produce, etc. The method is analytical in its nature, but is 
more than analytic, since it not only goes from the whole to 
its parts, but from the general to the particular. 



TEACIIIXG GEOGRAPHY. 465 

There are several advantages and disadvantages in this 
method. It is unsuitable to the beginner, as it inverts the 
law of mental development, from the particular to the gen- 
eral. It is not surprising that the recent attempts to intro- 
duce it into our elementary text-books on geography were un- 
successful. It is of great value to the advanced student, for 
it aids hiui in remembering and understanding the details as 
he sees their causes, and looks at them through their relation 
to a general scheme or law. It is not surprising that the 
method when first presented was so attractive to adult minds, 
and this will account for the fiict of the enthusiastic approval 
of certain text-books which did not meet expectation in the 
actual work of the school-room, 

III. Courses in Geography. — There should be three distinct 
courses in teaching geography. First, there should be a 
course of lessons for beginners, giving the general ideas and 
facts of the subject; second, there should be the detailed 
stud}^ of geographical facts; and third, there should be a 
course in the philosoph}' of geography. The first course may 
be called Primary or Elementary Geography; the second, 
Descriptive Geography; the third. Physical Geography. 

Primary Geofjrapliij. — The primary course in geography 
includes the leading ideas and facts of local and descriptive 
geography. It is designed to present to children thevr funda- 
mental knowledge of the subject. The instruction should be 
given orally in connection wifh illustrations, the globe, and 
outline maps, the pupils not being required to study the sub- 
ject from a text-book. 

The primar3' course embraces several distinct stages: first, 
a perceptive stage; second, a conceptice stage; third, a rejjy^e- 
sentative stage; and fourth, an explanatory stage. The first 
and second of these stages should be most prominent in the 
primary course; but the elements of the representative and 
explanatory stages are also to be presented. 

Descriptive Geo<jr<iplnj. — Plie second course embraces a 
20* 



466 METHODS OF teaching 

detailed description of the facts of geography. These facts 
are to be learned from text-books, and presented by the pupils 
in topical recitations. It is a detailed course in descriptive 
and local geography, following the attainment of the funda- 
mental ideas given in the primarj^ course. It combines both 
the analytic and synthetic methods of treatment, but employs 
l^rincipally the analytic. 

Physical Geography, — The third course includes the 
classification of the facts of geography into systems, and also 
the discussion of the causes of geographical phenomena, and 
the laws which govern them. It is the philosophical stage, 
and has been treated by American authors under the head of 
Physical Geography. 

•I. Teaching Primary Geography. 

The course in Primary Geograph}^ includes that elementary 
instruction which imparts the fundamental ideas and facts of 
the science. It embraces four distinct stages; the Perceptive, 
the Conceptive, the Representative, and the Explanatory 
stages. We shall first speak of the Principles of Instruction 
in this course, and then show the Methods of Teaching in each 
one of these four stages. 

I. Principles of Teaching. — There are several general 
principles which should guide us in teaching primary geog- 
raphy. These principles may seem very simple; but they 
have been constantly violated by teachers, and even by those 
who were regarded as intelligent and successful instructors 
of the branch. 

1. The course of indruction in primary geography should 
be given in the concrete. The geographical ideas should be 
presented to the mind of the learner by illustration, rather 
than b^^ description. This can be done by shoiving the ob- 
jects in nature, or by having models of them or pictures of 
them. When it is possible, the pupils should be shown the 
physical features; as a mountain, river, lake, island, cape. 



TEACHING GEOGRAPHY. 467 

isthmus, peninsula, etc. Many of these can be seen in mini- 
ature in nearly every neighborhood. We may go out by the 
riverside, or even b}^ the side of a small stream, and study 
geography. To take the pupils out into the yard after a rain 
and study geography in a " mud puddle," would be better 
than the ordinary abstract methods of the school-room. 

Good pictures of these objects will also be valuable in lead- 
ing pupils to clear conceptions of them. There is a piece of 
apparatus called the " geographical box," which would be very 
useful to beginners in geography. Such apparatus as were 
found at our late Centennial Exhibition indicate European 
methods of teaching geography, and would be most valuable 
in giving definite ideas on the subject. 

2. The course of instruction in primary geography should 
he first synthetic and then analytic. We should begin geog- 
raphy at home, in Ihe school-house and yard. From this we 
should go out to the surrounding fields and neighborhood. 
A short course on the map of the township, count}', and 
state may be given. We should then, and perhaps earlier, pass 
to a conception of the world as a whole, and studj' it ana- 
lytically. We first separate the surface into the two great 
divisions, land and water; then come down from the conti- 
nents to countries, states, counties, and townships. Thus, 
though we should begin with the synthetic method, we should 
be careful not to continue it too long, as the pupil will study 
the subject much more satisfactorily by the analytic method 
than by the synthetic method. 

3. The course of instruction in prirtiary geography should 
present facts before giving their classification and causes. 
This principle is in accordance with the natural laws of mental 
acquisition. It accords also with the historical order of the 
development of the science. The facts of the science were 
known long before their classification. Physical Geography, 
as presented in our text-books, is much more recent than 
Descriptive Geography. The attempt to invert this order, 



468 



METHODS OF TEACUING. 



•which has been made in some of our recent text-books, was a 
mistake ; and it is no wonder that the books needed earl}^ re- 
vision. The facts of local and descriptive geography must 
precede the attempt to generalize these facts into a system. 
There must be some knowledge of the individual rivers, 
mountains, etc., before a pupil is prepared to appreciate river 
systems, mountain systems, etc. 

4. The course of instruction in primary geography should 
begin ivith local and descriptive geography. The child is in- 
terested in and can readily understand and remember local 
geograph3^ He carries in his mind the picture of the map 
and the location of places, rivers, etc., and has little difticulty 
in remembering their names. To restrict the pupil, however, 
to local geograph}^, as is too often done, is a mistake. The 
teaching of mere names and places is a waste of time, for a 
large number must necessarily drop out of the memory. The 
drilling, day after da}', upon " map questions" without any 
description, is of little value to pupils. 

The description of places should be joined to the location 
of places. Interesting facts should be associated with the 
locations, for they will not only be of value themselves, but 
aid in fixing the location in the memory. That which was 
merely a " spot on the map" with a name, becomes a living 
reality to the pupil when interesting facts are associated with 
it. Tliese facts may be given and then the place located ; or 
Ave ma}' pass from the location to the descri[)tion. In prac- 
tice, the latter method will be usually found more convenient. 
Local geography may thus precede, but it should carry with it 
descriptive geography. After locating a country and point- 
ing out its principal cities, rivers, etc., the teacher should give 
and then require a description of its striking features, of its 
important events, of its people, their habits, employments, etc. 

5. The course of instruction in primary geography should 
include historical geography. In teaching geography, the 
leading historic events should be associated with the places 



TEACHING GEOGRAPHY. 4(i9 

described. As we describe the ditforent countries, reference 
may be made to the leading events of their histor3\ In con- 
nection witli the geography of the Okl World, facts concern- 
ing Cyrus, Xerxes, Alexander, Caesar, Charlemagne, Alfred, 
Wallace, Bruce, Napoleon, the Crusaders, the Spanish Arma- 
da, etc., may be related. In considering the Western Conti- 
nent, the story of its discovery, the course of the vessels, the 
place of landing, accounts of early settlements, encounters 
with the Indian tribes, etc., should not be omitted. The prin- 
cipal facts concerning the settlement of the several States of 
the Union may be presented in connection with their geo- 
graphical description; and in describing cities, mention should 
be made of the pi'incipal events that took place in them, and 
of the eminent men who have lived there. 

Celebrated buildings, like Girard College in Philadelpiiia, 
lead naturalh' to tlie statement of facts in the lives of their 
founders. St. Peter's at Rome and the Vatican could not be 
passed over without telling of Michael Angelo and Raphael. 
Westminster Abbey leads one to tell of its founder and the 
great men who sleep there ; Faneuil Hall will suggest the 
deeds of Warren and Adaius ; Independence Hall in Philadel- 
phia will remind one of the signers of the Declaration of 
Independence and the Bell of Libei-ty. The same method 
may also be applied to natural features. The Hudson River 
will remind us of Hendrick Hudson; Lake Champlain of 
Commodore Perry; Boston Harbor of the great tea-party; 
Lookout Mountain of Gen. Hooker ; Vicksburg of Gen. Grant, 
etc. Such an association of historic events with places will 
give a life and reality to the places, and link them to the 
memory by the tie of Interest. 

6. The course of instruction in primary geography should 
he practical. The teacher should aim to make the subject 
life-like and real. It is surprising how abstract and theoret- 
ical the knowledge of geography often is with young pupils. 
Their knowledge of the map is often merely the idea of so 



470 METHODS OF TEACHIXa. 

many lines and black spots on paper. The directions of 
countries from each other are often all confused b\^ the sec- 
tion map they studied, and the position of the seats in the 
school-room. Ask them to point to Europe, and they will as 
soon point north or west as east. We have seen children 
who were reciting on the map of Brazil point north for South 
America. 

The teacher should be careful also to present those facts 
which are the most important to be known. There is no use 
in remembering all the little rivers of Africa or the smaller 
towns of Europe, the exact areas of states, and the population 
of most of the cities. The teacher should also aim to connect 
the facts with everyday life.. Let him bring in a newspaper 
and read of events occurring in different places, and have the 
pupils to locate these places. Call attention to railroads, lines 
of steamers, etc. ; and show them liow we should travel by 
land or water from one place to another. Show also how one 
country is adapted for manufactures, another for commerce, 
etc. Endeavor to make "the subject a realit}' in the mind of 
a child, and not a mere collection of words or abstract marks 
on a map. 

"I. The course of instruction in primary geography should 
be given orally. For primary pupils no text-book is needed. 
To have them study the subject in a text-book at first, is to 
have them commit words instead of learning geograph3\ The 
teacher needs a globe and outline maps, but no text-book for 
the first year or two in teaching primary geography. The 
ideas of geographj- are to be presented b}' real objects, or by 
models or pictures of them. Localities are to be pointed out 
on the map and globe, and the descriptions given verbally by 
the teacher and remembered and repeated bj' the pupil. After 
stating a fact, the pupil should repeat it, and the facts given 
in one lesson should be repeated at the next lesson. Facts 
learned in this way will possess an- interest for the pupil and 
make a permanent impression on liis memory. 



I 



TEACHING GEOGRAPHY. 471 

II. Method or Teaching. — We now present the course of 
instruction in Primary Geography. The lessons should be 
given in the following order: 1. The Perception of geograph- 
ical facts; 2. The Conception of geographical facts; 3. The 
Representation of geographical facts; 4. The Explanation 
of geographical facts. 

1. The Perception of Geographical Facts, — The first 
step in teaching geography is to give the pupils geographical 
ideas through the senses. If is a geographical lesson on that 
which the pupils can observe for themselves. It employs the 
objects of the world around us, or models or pictures of them. 
This stage will include lessons on Land, Water, the Soil, the 
People, Animals, Plants, and Minerals. 

Nature of the Lessons. — Lessons on Land will include les- 
sons on hills, mountains, plains, islands, capes, isthmuses, etc. 
Lessons oa Water will include springs, ponds, rivers, lakes, 
bays, straits, etc. Lessons on Soil will include the different 
varieties of soil found in the neighborhood. Lessons on the 
People will include the looks, manners, habits, education, re- 
ligion, etc., of the people of the town or vicinit3^ Lessons 
on Animals include the domestic animals and the principal 
wild animals, the birds, the insects, etc., found in the vicinity. 
Lessons on Plants include the trees of the 3'ard, orchard, and 
forest, and many of the principal plants and flowers. Les- 
sons on Minerals include quartz, limestone, sandstone, and 
such other minerals as are common to the place, or of which 
specimens can be obtained. 

The 3Iethod. — The method of teaching the primary ideas 
and facts of geography should be concrete and deductive. 
The objects, or models or pictures of th^m. should be pre- 
sented to the pui)il, if possible. We should also pass from 
the ideas to the terms which express them; and from a 
clear idea of the meaning and use of a term to its definition. 

Lessons on Land and Water. — The pupils should be 
taken out of doors and shown the divisions of land, and be 



472 METHODS OF TEACHING. 

taught their names. They ma}' be shown a hill, or a moun- 
tain, if there is one in the neighborhood. They should be 
taken down to the river that they may see an island, a cape, a 
peninsula, an isthmus, etc. The teacher should also show the 
different divisions of water and give their names. A " geo- 
graphical box," representing these divisions of land and water, 
will be of great advantage to the pupil. Such a box can be 
easily made, with depressions and elevations carved in the 
wood, and water poured in it, to represent the different phys- 
ical features. The divisions of water and land can also be 
represented on the blackboai'd. A little water poured upon 
the school-room floor can be made to serve the same purpose. 

Other Lessons. — Pupils should be shown the different 
varieties of soil, as sandy, clayey, etc.; their adaptation to 
different kinds of crops, etc. They should be taught to ob- 
serve and describe the peculiarities of the people, their lan- 
guage, customs, occupations, interest in education, religious 
beliefs and customs, etc. They should also be taught the 
names of all the ordinary trees of the neighborhood, and to 
distinguish them b}' their leaves, bark, and the grain of the 
wood; and also the names, habits, and peculiarities of the 
animals of the neighborhood, as is indicated in the system of 
object lessons. Such a drill will give knowledge which will 
serve as the basis for learning about such things distant from 
home, and enable the instruction to pass from the known to 
the unknoivn. The student-teacher will exemplify this stage 
in a model lesson. 

2. TJie Conception of Geographical Facts. — The Percep- 
tion of geographical facts should be followed by the Concep- 
tion of those which cannot be perceived. From a knowledge 
of that which the pupils can see, they should be led to a 
knowledge of similar things of which they can conceive. The 
objects of perception thus become the basis of objects of con- 
ception. These two stages may to a large extent go hand in 
liand in actual instruction. 



TEACniXG GEOGRAPHY. 47.) 

Nature of Lessons, — The lessons on Land include moun- 
tains, plains, prairies, deserts, table-lands, volcanoes, etc. 
Lessons on Water include rivers, bays, gulfs, straits, chan- 
nels, lakes, oceans, etc. Lessons on People may include the 
Indians, Hindoos, Chinese, Japanese, Esquimaux, Africans, 
etc. Lessons on Animals include lions, tigers, bears, wolves, 
monkeys, elephants, alligators, the ostrich, the condor, the 
eagle, etc. Lessons on Plants include the tea-plant, coffee- 
plant, cotton-plant, bread-fruit, banyan-tree, cinnamon-tree, 
etc. Lessons on Minerals include iron, zinc, copper, lead, 
coal, gold, silver, diamonds, etc. 

Method of Teaching. — The method of teaching should, so 
for as possible, pass from the conception of the known to the 
conception of the unknown. Beginning with some visible ob- 
ject, the mind may be led to conceive the invisible. The facts 
of sense thus become the basis of the ideas of conception ; the 
thing seen becomes the representative of the thing to be con- 
ceived. By means of the imagination we, as it were, trans- 
mute the real object into the ideal conception. 

Lessons on Land. — To give a pupil an idea of a Mountain, 
let him think of a hill which he has seen, and imagine it to 
grow higher and higher until it is half a mile, a mile, two 
miles, three miles, etc., high ; its top crowned with clouds 
and on its summit resting perpetual snow. In this manner a 
pupil ma}- obtain quite a definite idea of a mountain. Then 
let him imagine it to begin to stretch out further and further 
awa}^ until it reaches many miles beyond the horizon; this 
will give an idea of a mountain range. 

To conceive of a Prairie, have the pupil think of a meadow, 
and then imagine it to begin to spread out in ever}- direction, 
further and further away, until it reaches many miles in 
extent ; let him imagine tlie grass growing as high as his head, 
adorned with a profusion of rich flowers, and inhabited by 
prairie birds, herds of buliUloes, and droves of wild horses. 
It will add interest to the conception to describe a prairie 



47-1 METHODS OF TEACHrXG. 

on fire, the flames traveling with great speed, and bnffaloes 
and droves of wild horses flying in fright before them. 

A Desert can be conceived by beginning with a small level 
area of sand, and imagining it to spread out in every direction 
until it covers an extent of many miles — a waste of parched 
sand, dotted here and there with bright green oases. They 
may also be led to see the caravans crossing the desert, with 
the camels and horses, now stopping at an oasis, and now 
overtaken by a storm of sand from which they can escape 
only by dismounting and covering their faces, and by which 
they are "often buried in a sandy grave. 

Other Lessons. — In a similar manner, a rivulet may be en- 
larged into a river, a pond into a lake, a lake into an ocean, so 
wide that it will take ships weeks to sail across it. Vivid 
conceptions of the people may be given by life-like descrip- 
tions of them, as the Chinese with their habits so opposite to 
ours, the Hindoos, with their dreamy beliefs and cruel relig- 
ious rites ; the Indians, with their wigwams, bows and arrows, 
and war dances ; the Esquimaux, with their ice-huts, dogs, and 
sledges. Ideas of animals, plants, etc., can also be given by 
descriptions and pictures of them. 

Adaptation. — These facts should be adapted to the capacity 
and taste of the pupils. The teacher will readilj^ see what 
things are interesting to the young learner, and will be able 
to tell how far to enter into details in his lessons. Much of 
the interest will be due to the manner of the description; and 
it will afford the teacher an excellent opportunity to cultivate 
an easy and artistic method of describing objects. Let it be 
remembered that it is the author's opinion that no teacher is 
competent to teach geogra2:>hy until he is able to give such de- 
scriptions. Let the student-teacher show how to give the 
lesson and extend the method to other things in the course. 

3. The Representation of Geographical Facts Tlie 

next step in geographical instruction is the representation of 
geographical ideas on paper in the form of a map. This stage 



TEACHING GEOGHAPnY. 475 

includes both the Drawing of Maps and Lessons on Maps. 
It begins with giA'ing an idea of direction, then showing how 
to indicate direction, then the malving of a map, then the 
study of outline maps. 

Direction. — The first thing is to teach a pupil the different 
directions. We may do this b}'^ having him stand with his 
face to the north, and arms extended, the right hand pointing 
to the east, and the left hand to the west. The rising and 
setting sun will indicate the east and west; and it will be well 
to have the pupil fix the north bj' observing the position of 
the North star in the evening. 

Indicating Directions. — The next step is to indicate these 
directions. Draw a north and south line on the floor, and 
across it an east and west line; and call attention to the direc- 
tion of objects from the point of crossing. Then draw these 
lines on a liorizontal slate or piece of paper, place the pupil at 
the south end of the slate or paper, and lead him to see that 
the side next to him is south; the side from him is north; the 
right-hand side, east; and the left-hand side, west. 

Melative Directions. — These are now absolute directions ; 
the next step is to lead to the idea of relative directions. To 
do this, we represent on slate or paper some of the objects in 
the school-room, indicating their directions from one another. 
"We then gradually change the position of the §late or paper, 
still calling attention to the fact that the right hand indicates 
east, the left hand west, the upper part north, etc., and that 
the objects represented have the same relative directions. 
Great care is to be exercised in this lesson, that the pupil may 
have a correct idea of the relative directions indicated on the 
map. 

Making a Majy. — The next stop is to make a map of the 
school-room,' locating the different objects, the teacher's desk, 
the platform, the stove, etc. Then make a map of the school- 
3^ard, locating the objects in it. Then include in the map the 
neighboring fields and the different farms, locating the roads, 



476 METHODS OF TEACHING. 

the woods, the farm-houses, the barns, etc. Then let the pupils 
draw maps of their own homes, their gardens, the streets of 
the village, indicating the principal buildings, etc. They may 
also draw imaginary maps. 

Lesson on 3Icips. — We should next pass to the map of the 
township, county, or state, or a map of the United States or 
the world, as the teacher prefers. The pupil should then have 
a regular drill on maps, and leai-n what is called Local Geog- 
raphy. The lesson in local geography will include : 1. The 
pointing out and naming of localities ; 2. The description of 
geographical features ; 3. Some of the principal historical 
events relating to countries and places. 

3I(f2) Drawing. — The elements of Map Drawing may now 
be introduced. The, first lessons should be entirely by imita- 
tion. No method of triangulation or the use of construction 
lines should be used. The pupil will look at the map, and 
then try to draw the map from memory. At first, if he wishes, 
he may put a thin piece of paper over the map of an atlas and 
trace the outline. It will aid in giving a more definite idea 
of the contour, and will serve as an introduction to construct- 
ing a map from memory. Maps should be drawn on the 
blackboard as well as on paper. 

4. The Explanation of Geographical Facts. — The pupil is 
now prepared for the Explanatory Stage of Geography. This 
includes the explanation of geographical facts and phenomena, 
especially those pertaining to the astronomical elements of 
geography. It includes the Form of the Earth, the Motions of 
the Earth, the lines of Latitude and Longitude, the Circles on 
the globe, including the Equator, the Tropics, the Polar Cir- 
cles, and the Zones. 

Form of f lie Earth. — The teacher should begin by calling 
attention to the apparent form of the earth. Then tell them 
it is round like a ball, and show its form by a globe. Give 
also some of the simple proofs of its rotundity, as the appear- 
ance of a vessel approaching or receding from the shore, the 



teach;ng geography. 477 

sailing around it, etc. A magnetic globe will illustrate the 
first proof. We then show that the surface of the earth con- 
sists of land and water, point out the land and the water, name 
the different grand divisions of land and water, and explain 
their form, position, etc. 

The Equator, etc. — The next step is to call attention to 
the various circles of the globe and explain their uses. The 
equator, parallels, and meridians should be introduced by 
showing their use in locating objects. To illustrate, suppose 
we mark an object on the globe; we must look over the entire 
surface to find it. But suppose we draw a line around the mid- 
dle of the globe and sa}^ the object is above or below this line, 
then you need look over only one-half of the surface to find 
it. Then suppose we draw lines parallel to this line, which 
we call the Equator, and say the object is on one of these 
lines ; now you need look only on this line to find it. Sup- 
pose now we draw a line from the top down through the object ; 
we can locate it exactly by the intersection of these lines, or 
by saying it is so many units above the equator and so many 
units to the right or left of a given line. 

We then give their names, equator-, parallels, and meridiariH, 
and explain the division of the circle into degi'ees, etc. We 
then drill in finding latitude and longitude of places, and in 
finding places by the latitude and longitude. We may also 
show them that the extent of latitude is 90°, and of longitude 
180°, and lead them to see what places have no latitude, no 
longitude, no latitude and longitude. In this way pupils 
may be given a much clearer idea of the nature and use of 
parallels and meridians as locating lines than they usually 
possess. 

Motions of the Earth. — The next step is to teach the two 
motions of the earth. The diurnal motion may be illustrated 
by the revolution of a globe on its axis, showing the phe- 
nomena of da}' and night, sunrise and sunset. The apparent 
motion of the sun may be illustrated b}' the common experi- 



478 METHODS OF TEACHING. 

ence of the apparent motion of a railroad train when at rest. 
The annual motion and its effects ma_y be illustrated by a 
tellurium, or in its absence, by an apple or a pumpkin, carried 
around a lamp representing the sun. The common globe may 
also be carried around some object representing the sun, care 
being taken to keep the axis always parallel to its first posi- 
tion, inclined about 2oi- degrees. A very clear idea of the 
change of seasons, etc., can be given in this way. 

Aocis of the Earth. — The next step is to call attention to 
the axis of the Earth, as the centre of its motion. Explain 
that this is inclined to the orbit about 23^°, that it is always 
parallel to a given position, and that the ends are called 
Poles, etc. 

Circles and Zones. — The next step is to explain the trop- 
ical and polar circles. This may be done by the tellurium, or 
by carrying the globe around a lamp, orb}" charts or diagrams 
on the board. Let them see that in one part of the orbit, the 
sun shines 23^° over one pole and lacks 23^° of reaching the 
other pole, which will fix the polar circles. Let them see 
that in one position, the sun is exactly over a point 23^° 
above the equator, and in another over a point 23i.° below the 
'equator, which will fix the tropical circles. Then explain the 
meaning of a zoiie or belt, and let them see that the cold or 
frigid zones are 23^° wide ; that the hot or torrid zone is 
23i° + 23i°, or 4^°, wi'de; and that to find the width of each 
temperate zone, we add the width of the frigid and the torrid 
on one side of the equator, and subtract the sum from 90°; 
thus, 23i° + 23^°=47°; 90°— 4t°=43°. 

L€sso)ts on Zones.— Ijcssows may then be given on the 
productions of the different zones; their animals, trees, etc.; 
the difference in the inhabitants, their occupations, etc. 
The appearance of the moon, stars, and sun in circling the 
heavens, the long twilight, the long nights of winter, etc., of 
the frigid zones, will be interesting to the pupils ; also an ac- 
count of the efforts to reach tlie Xortli Pole. 



TEACHING GEOGRAPHY. 479 

Memarks. — Such a course should be giveu in connection 
■^■ith the conceptive and representative stages of the subject. 
The lessons, as indicated in these stages, may be continued 
several months, indeed, in a graded school they should be 
continued for several 3'ears, before the pupil takes a text-book 
to stud}'. The principal part of the course will be the local 
and descriptive elements ; the maps of all the countries should 
be studied, and the most interesting facts stated to the 
pupils. 

If the pupils have a book, containing a few of the more in- 
teresting facts, to read (not to commit for recitation), it will 
add interest to the lesson, and give them something to look 
at outside of the recitation. The teacher should make out an 
outline of a little text-book on geography, and follow this 
course in his instruction. It will add greatly to the teacher's 
knowledge and to the interest of his pupils. Indeed, a 
teacher who is not able to carry out such a course in geog- 
raphy, is so far not thoroughly prepared to teach the subject. 

II. Teaching Advanced Course in Geography. 

The Advanced Course in Geography embraces a full school 
course in local and descriptive geograph}'. It includes the 
formal study and recitation of the subject. The pupils are 
expected to study the lesson in a text-book, and come to the 
recitation prepared to recite what they have learned. We 
shall speak briefly of the Principles of Instruction in this 
course, and of the Methods of Teaching the course. 

I. Principles of Teaching. — There are several principles 
by which the teacher in the advanced course in geography 
should be guided. The tliree most important are the fol- 
lowing: 

1. The course in advanced geography should be analytic 
rather than synthetic. We should begin at the world as a 
whole,, and study from the w^hole to its parts, or we should 



480 .METHODS OF TEACHING. 

begin with a larger division and come down gradually to the 
smaller divisions of countries. The course should pi'oceed 
from the general to the particular; from the whole to its 
parts. 

2. The course in adoanced geography should extend to the 
classification of geographical facts. The child begins geoa:- 
raph}^ with details, but it will be of advantage to group these 
details into classes or S3'stems of facts. Thus, after a knowl- 
edge of several of the particular rivers of a country, we may 
classify them into river systems, and study them as such. 
So from a knowledge of individual mountains we may pass to 
their classification into systems, and study the mountain 
systems of the globe. The method to be pursued is thus in- 
ductive rather than deductive. 

3. The course in advanced geography may also include an 
inquiry into the causes of geographical phenomena. The facts 
of geographj^ will include some of the striking facts and phe- 
nomena of the globe, and the child will naturally inquire after 
the causes of them; and it willbe well to gratify this inquiring 
spirit. We maj' explain the causes of volcanoes, earthquakes, 
hot springs, ocean currents, etc. We may call attention 
to the circumstances which determine the location of cities, 
the causes of the prosperit}^ of nations, the reason for certain 
industries, etc. Such instruction may be mingled with the 
facts of the course, or it may be presented at the close of the 
book, or in the form of a general review of the subject. 

II. Methods op Teaching. — The course in advanced geogra- 
phy should include the following subjects : 1. Definitions ; 
2. Description ; 3. Lesson on Maps ; 4. Drawing Maps ; 5. 
Interesting Facts; 6, Imaginary Travels; T. Geographical 
Outlines; 8. Classification and Causes of Geographical Facts. 

1. Definitions — Pupils should be required to give defini- 
tions of the principal terms used in geography. Thus, they 
should be required to define a river, a lake, an ocean, a hill, a 
mountain, an island, etc. In these definitions we cannot 



TEACHING GEOGRAPHY; 481 

nbva_ys pretend to scientific accuracy, but it is tbou(2:ht to be 
uf advantage to the student to give statements approximating 
such definitions as closely as possible. The ideas of these 
geographical objects were obtained in the elementary course; 
tlie pni)il should now be required to express these ideas in the 
form of definitions. 

2, Descriptions. — The pupils should also be required to 
learn the descriptions as given in the text-book, and to present 
the same in the recitation. They should not commit the text 
verbatim, but be encouraged to give the matter partly in their 
own language. The recitations should be largely topical, 
though points omitted ma}' be brought out by questions. The 
descriptions may be given in connection with the map or with- 
out it. The pupil should learn to describe awa}' from the 
map as well as on it; for in his reading he will not have the 
map before him, and he must learn to conceive geographical 
localities without the map. The pupils may be encouraged to 
give any fjicts bearing upon the subjects considered, not found 
in the text-book used in the school. 

3. Lessons on Maps. — In connection with the descriptions 
there should be constant lessons on maps. Pupils should be 
thoroughly drilled in local geography, for they need to know 
the location of places. For this purpose pupils should have 
atlases, and there should be outline maps in the school. 
These lessons on maps may be given in several different ways. 
First, the pupil may stand at the outline map, and with a 
pointer i)oint out and name localities. Second, one pupil ma'y 
point out and another pupil may name the places indicated. 
Third, one pupil may stand at his seat and name certain 
places, and another pupil standing at the map, raa}^ point them 
out. Fourth, the teacher ma}^ point out and the pupils name, 
or the teacher name and the pupils point out places. Care is 
to be taken that the map is made a means to and not the end 
of geographical knowledge; a knowledge of the position of 
so many lines and spots is worthless, unless they are sug- 
gestive of the realities of nature. 



482 METHODS OF TEACHIXQ, 

4. Dratving Ma^ts. — The pupils should be required to draw 
maps as well as to study them. There are several reasons for 
map-drawing in the study of geography. First, it aids the 
pupil to fix the physical features in the memory, by requiring 
a closer and moye minute observation than is necessary for 
mere description. Second, it begets a habit of close and ac- 
curate observation in the study of maps. Third, it gives skill 
in representation, which may be of advantage to the pupil in 
many circumstances in life. 

Methods. — There are two methods of map-drawing ; that of 
simple imitation and that of constructio/i lines. By the 
former method, the pupil loolcs closely at the map, and then 
endeavors to reproduce it by merely imitating the model. 
By the other method, certain lines are drawn to guide the 
pupil in obtaining the correct form and outline. With j'oung 
pupils we should depend mainly on imitation; with older 
pupils construction lines may be used with advantage. The 
S3^stem of construction should, however, be simple; the com- 
plicated systems of some authors are a waste of time. 

5. Interestiiig Facts. — The teacher should add to the text 
interesting geographical and historical facts. In no subject 
taught in the common schools is there such a fine opportunity 
for the teacher to use liis general knowledge, and awaken an 
interest in the study by additions to the text-book. The 
knowledge gained by travel or reading descriptions of foreign 
countries, can all be made available in the geography class. 
The study of good works on travel will be of great advantage 
to the geography teacher; and we recommend him to read 
such works extensivel3^ Photographs of celebrated places, 
cities, buildings, natural scenery, etc., will add greatl}' to the 
interest of pupils. There should be a stereoscope and a col- 
lection of views in every public school. 

6. luiafjinavfj Travels. — Much interest can be awakened 
b}^ means of imaginary' travels and vo_yages. These ma}' be 
given in several different ways. First, the teacher may inquire 



TEACHING GEOGRAPHY. 483 

how we may travel from one place to another, as from New 
York to Chicago; and have the pupils point out and desci'ibe 
the trip. Second, the teacher can describe a trip or voyage, 
giving a description of the places at which he stops, not their 
names, and have the pupils name the places from the descrip- 
tion. Third, the pupils may be required to prepare descrip- 
tions of imaginary travels and voyages, the class naming the 
places as they are described. 

1. Geograpliical Outlines. — The pupils are now ready to 
classify their knowledge of geography, and they should be re- 
quired to commit and use an outline in describing the different 
countries. Such an outline will be valuable in aiding them to 
collect and remember geographical facts. With such an out- 
line, they can acquire the knowledge from different books, if 
it is desired; all that is needed is that the facts they know be 
grouped according to the same method. 

The following is a simple and convenient outline. It ma}' 
be used in connection with any country or state, by making- 
such siiglit modifications as the subject naturally suggests. 

rl. Positioa. fl. Appearance. 

J 2. 



Position, etc. \ 2. Extent. 4. The People \ 2. Customs. 

( 3. Contour. (. 3. Pursuits, etc. 



Natural Features 



!1. Land. ( 1 . Cities and Towns. 

2. Water. 5. Their Works ] 2 Public Works. 
3. Climate. ( 3. Buildings, etc. 



fl. Animal. 
2. Vegetable. f 1 . Government. 

3. Mineral. 6. Institutions \ 2. Education, 
o. x-iuuuci^. -^ rl. Animal. 1 3. Religion. 

2. Artificial ] 2. Vegetable. 

( 3. Manufactures. 



IV. Teaching Physical Geography. 

Definition Physical Geography, in its literal sense, treats 

of the physical features of the earth, that is, of the earth as 
unmodified by man. In this country, however, the term has 
acquired a special signification, meaning the philosophy of 



484: 



METHODS OF TEACHING. 



geography. In this sense, it treats of the classification of 
geographical facts into systems, and presents the laws and 
canses of these facts. 

3Iethods of Teaching. — Little need be said concerning 
methods of teaching the subject. The pupil will study it from 
a text-book and recite it. The general recitation should be 
topical ; but the teacher should see by questions that the pupil 
understands the subject. Illustrations on the blacliboard 
should be constantly required, and some charts and apparatus 
will occasionally be of service. The best books we have ex- 
amined upon the subject are Warren's, Mitchell's, and Hous- 
ton's; but Guyot's Earth and Man should be in every teach- 
er's librar}'. 

Divisions. — The subject may be treated under the divisions 
indicated by the following Outline: 



[. Earth as a Planet. 


III. The Water. 


1. Form and Size. 


1. Continental Waters. 


2. Motions and Orbit. 


1. Springs. 


3. Circles and Zones. 


2. Rivers. 


4. Times and Seasons. 


3. Lakes. 


[. The Land. 


2. Oceanic Waters. 


1. Inside of Earth. 


1. The Ocean. 


1. Internal Heat. 


2. Ocean INIovements. 


2. Volcanoes. 


3. Ocean Currents. 


3. Earthquakes. 


IV. The Atmosphere. 


2. Outside of Earth. 


1. Properties. 


1. The Structure. 


2. Temperature. 


2. Distribution of Land. 


3. Moisture. 


3. General Forms. 


4. Winds. 


4. Special Forms. 


5. Climate. 


'. Organic Life. 


6. Storms. 


1. Botany. 


7. Electric and 


2. Zoology. 


Optical Phenomena. 


3. Ethnography. 





HISTORY. 



CHAPTER L 

TEACHING HISTORY. 



HISTORY is a narration of the events which have occurred 
among mankind. It describes the past actions of man- 
kind, the rise and fall of nations, and the changes in the polit- 
ical and social condition of the human race. In its higher 
departments, it seeks also for the causes which have been 
operative in pi-oducing these events. The term is derived 
from the Latin historia, which is from a Greek word of nearly 
the same form, meaning to learn or know from inquiry. The 
word was first used b}' Herodotus near the beginning of his 
work; and it is supposed that he thus fixed the sense in 
which it has since been used. 

Divisions. — History is divided into two great branches ; 
the Fads of Histori/, and the Philosophy of History. The 
Facts of History embrace the orderly and systematic state- 
ment of the events that have occurred in the lives of indi- 
viduals and nations. The Philosophy of History endeavors 
to ascertain the causes which have contributed to produce the 
diff'erent changes in society and nations, and from these to 
predict the future condition and destiny of mankind. 

History is also divided into Ancient, Mediseval, and Modern 
History. Ancient History is considered as ending about 470 
A. D., the date of the destruction of tiie western division of 
Mie Roinnn eniiiire; Mediieval History, or the history of the 
Middle Ages, extends from 476 A. D., to very near the dis- 
covery of America by Columbus ; Modern History begins at 

(485) 



486 METHODS OF TEACHING. 

or near the discovery of America, and extends down to the 
present time. History is also divided into Saa^ecl and Pro- 
fane; and still other divisions are sometimes made. 

The Facts. — The Facts of History differ in some respects 
from the facts of the other sciences. They are facts that 
have occurred in the past and are not, therefore, subject to 
pi-esent obse'rvation. They are thus known only through tes- 
timony^, either oral or written, and must l^e accepted on au- 
thority. .They are also connected by the relation of time, 
rather than by that of kind and quality, like tlie facts of the 
other sciences. They arc the acts of free agents, proceeding 
from the operation of a spiritual being not governed by inex- 
orable law, like the forces of nature, but which is a law unto 
itself, and which freely cliooses its course among the external 
cii'cumstances that are the conditions of its actions. 

The Philoso2)hy. — History was formerly only a recital of 
the actions of mankind ; but recently attempts have been 
made to form a Philosophy of History. The great thinkers 
of the world have looked over the drama of human experi- 
ence, and have endeavored to ascertain the influences which 
have been operative in moulding the events of the world. 
The object has been to trace the action of causes and deduce 
certain principles which may serve as a guide to statesmen 
and rulers in conducting the affairs of nations. Yiewed in 
this light, history has been happily styled "philosophy teach- 
ing by example." 

Systems. — Among these, three great classes of thinkei's 
have presented three distinct methods of explaining the exist- 
ence of historic events. These three theories are denomi- 
nated the Materialistic, the Spiritualistic, and the Theistic 
theories. The Materialistic Theory holds that the events of 
history ai-e caused by the physical conditions b}' which man 
has been surrounded. The Spiritualistic Theory holds that 
man is a free agent and lias deterrauicd his own actions in 
view of the circumstances under which he was placed. Tlie 



TEACIIIXG HISTORY. 487 

Tlioistic Theory maintains that man's actions have been deter- 
mined by conditions imposed upon him by God. 

Difficulties. — History i^resents many difficulties not met 
with in the other branches of knowledge. Many of the events 
occurred so far back in the past that it is impossible to know, 
in many cases, Avhether what is recorded is true. Many of 
them have been handed down by tradition, and are, no doubt, 
partially if not wholly false. The prejudices of mankind 
have so warped their judgment and statement of the events 
of their times that it is difficult, if not impossible, to know 
what was the truth in particular cases. Several long-believed 
historical statements have recently been shown to be untrue; 
and we know not how many things we believe to be facts that 
never occurred. So great are these difficulties that Walpole 
declares "all history to be a lie;" Napoleon said, " History is 
but a fable agreed upon ;" and Dumas remarks that " Truth is 
very liable to be left-handed in history." 

In the philosophy of history, the difficulties are still 
greater. The motives of different men are so different, the 
effects of circumstances on different persons are so diverse, 
the influences of the external world on people vary so greatly 
with their intellectual development and the moral influences 
thrown around them, that the attempt to ascertain the causes 
of men's actions, and to predict the future condition of the 
race, is a problem of surpassing difficulty. 

Historical IForJcs The works on the facts of history 

may be classified into the Fragments of History, TJniA'ersal 
Histoi'y, Compends of History, and Detailed History. Frag- 
ments of Historj^ embrace the events of a particular period 
or the life of some particular person. Universal History pre- 
sents an account of the principal nations of the globe in a 
connected ijarrative. Compends of History embrace a brief 
and comprehensive narration of the events of a nation or of 
several nations. Detailed History contains a full account 
of some nation, people, or particular person or event. 



488 METHODS OF TEACHING. 

Value of H'lHtory, — The teacher should have a clear iflea 
of the relation of a subject of study to a general system of 
education. He should know its object and importance, that 
he may be able to teacli it with appi'eciation and skill. A few 
words will therefore be said concerning the valne of the study 
of history. 

1. The study of history gives culture to the memory. 
History consists of a narration of facts. These facts are to 
l)e committed to memory; they are valuable to the student 
only as they are retained in the mind. They cannot be 
thought out, they can only be acquired and remembered ; hence 
historj'^ is especially a memory study. Only a person with a 
good memor}' can become well versed in history; and among 
all the studies history stands first in giving exercise and cul- 
ture to the memor}^, 

2. History gives culture to the imagination. It deals with 
events and incidents, and these rise up before the mind as 
pictures of human action. To study histor}' properly, the 
student must imagine the scenes as they are portrayed by 
the pen of the historian. The events of the past should pass 
before the mind like the pictures of a i)anorama. This brings 
the imagination into vigorous activity and affords it a fine 
field for its operations. Indeed, no school study affords such 
an opportunity for the culture of the imagination as history. 

3. History cultivates the power of probable reasoning. Not 
onl_y arc the facts of history to be remembered, but their 
causes are to be ascertained and the probable effects esti- 
mated. This requires what is called probable reasoning. 
The historian must weigh consequences, estimate the effect 
of conflicting and interacting causes, and with a sure pre- 
vision endeavor to read the future result. History thus 
trains that power which prepares for thinking correctly on 
the practical affiiirs of life, to a greater extent than any 
other subject, unless it be Ethics or Political Economy. 

4. The study of history gives moral culture. History' deals 



TEACHING HISTORY. 489 

with tlie actions of mankind ; and these actions contain a 
moral element. We see the motives which inspire and the 
results which flow from these actions. We see the conse- 
crated labors of the good, the devotion of the patriot, the 
fortitude of the martja*, and our souls in admiration are lifted 
up into a higher plane of moral feeling. We see the mean- 
ness of the ignoble, the craft and falsehood of the unprinci- 
pled, the corruptions of the base and degraded; and the soul 
turns instinctively av^'ny from the low and vicious to the pure 
and virtuous. Tlie noble and the ignoble, the generous and 
the selfish, as the}' stand contrasted in the pages of history, 
awaken in us admiration for the right, and detestation for the 
evil. We long to emulate the deeds of heroes and patriots, 
and thus a desire for good and noble actions is excited in the 
mind. For moral culture, a boy should go to historj' rather 
than to moral philosophy. 

5. T/ie study of history prepares for citizenship. In it we 
read of the value of wise and wholesome laws, and of the politi- 
cal vices that sap the foundations of society and the state ; 
and thus learn what to do and what to aA'oid to secure the 
good and the honor of one's countr3\ This knowledge is 
especially useful in a republic, where every man is a voter. 
The freeman's ballot should be an intelligent ballot ; an igno- 
rant ballot is a curse to a republic. Everj^ voter should be 
familiar with the past history of his country, and sliould be 
guided in his voting by lessons of wisdom learned from the 
actions of the wise men who have shaped the destinies of the 
nation. The flame of patriotism is kindled and nourished b}'^ 
the study of the patriotic deeds of our forefathers ; and the 
object of school studies is to make patriotic citizens as well 
as wise and virtuous men. 

Divisions fov Teaching. — For the purpose of instruction 
we divide the subject of history into three parts : 1. The Ele- 
ments of History ; 2. The Advanced Course in Histor}-; 3. 

The Philosophv of History. We shall give a brief discussion 
21* 



490 



METHODS OF TEACIIIXQ. 



of the methods of teaching the Elements of History and the 
Advanced Course in History ; but the Philosophy of His- 
tory, not being appropriate to the public school, will not be 
considered. 

I. Teaching the Elements of History. 

By the Elements of History we mean such elementary 
instruction as every young pupil is prepared to receive before 
it is thought best to have him study and recite the subject 
from a text-book. It embraces a large number of interesting 
events and incidents which are suited to the taste and capa- 
city of young pupils. We shall mention a few Principles of 
Instruction to guide the teacher in his work, and then briefly 
indicate the Method of Instruction. 

I. Principles of Instruction. — The teacher of the Elements 
of History should be guided by the following principles. The 
necessity of these principles is enhanced by the fact that they 
have been frequently violated ; and that the vicious methods 
used have generated a distaste for the study in the minds of 
learners. 

1. Instruction in the elements of history should he given 
orally. No text-book should be used in the early lessons in 
history. The pupil is not to be required nor permitted to 
prepare and recite a lesson from a text-book. Tlie child who 
attempts to learn histor}^ from a text-book usually commits 
the words but learns little history ; the histoi'ical fact escapes 
his attention in his effort to commit and recite the words of 
the book. The teacher is to give t)ie facts orally, and haA'e 
the pupil remember and reproduce them. There is no objec- 
tion to the pupils reading a book on the subject; but the com- 
mon method of having young pupils recite lessons from a text- 
book should be discontinued. 

2. Instruction in the elements of history should begin at 
home. We should first give the pupil some knowledge of the 
history of his own country. He will be more interested in the 



TEACHING HISTORY. 491 

events occurring in his own land, and will understand them 
better. From the CA^ents occurring here, he will naturally de- 
sire to pass to the events which trans^Dired in other countries. 
Thus, from the history of America we are naturally led to the 
history of England and France; from these we pass naturally 
to Rome and Greece, which in their turn lead us to Syria, Per- 
sia, and Judea. It is thus clear that we should begin at home, 
pass to the history of related countries, and then from the his- 
tory of particular counti'ies to General Histor}'. 

3. The basis of instruction in the elements of hisfonj is 
biography. Children are mOre interested in persons than in 
events. What a man did; how he struggled and suffered and 
triumphed ; what he accomplished or how he failed ; — all this 
is of absorbing interest to a child. Primary history should, 
therefore, be largely personal. Biography is the soil out of 
which the tree of history is to grow for a beginner. The 
events of history are to be made to cluster around some per- 
sonal character; the life of some great leader or patriot is to 
be the centre from which we are to view the historic story. 

4. The first lessons in history should be presented in the 
form of narratives. Children are fond of story-telling. 
They will listen for hours absorbed in the relation of inter- 
esting personal events. It was thus that the traditions of 
nations were sung or rehearsed in the early days of the 
world. Our fathers refer with delight to the revolutionary 
stories which were told to them, when children, by their 
sires or grandsires, around the fire of a winter evening. 
Such incidents linger in the memory, and cultivate a taste 
for historic knowledge, which in the present generation seems 
to be on the wane. Let the teacher fill his mind with the 
stories of history, and relate them to his pupils, and he will 
find breathless attention and a growing interest in historic 
knowledge. 

5. Instruction in the elements of history should be given in 
connection icifh geography. History and geography are 



492 METHODS OF TEACniNQ. 

closel}' related, both in their nature and interest. To know 
the location of a country and the character of its people, is 
to awalven the inquiry, When was it settled? by whom? and 
what has contributed to its growtli and development? His- 
tory and geography should, therefoi'e, go hand in hand in 
primary instruction. We should give historic facts in con- 
nection with our lessons in geography, linking the historic 
events to the localities of the maps wliich we name and 
describe. 

II. Methods of Teaching. — These general principles indi- 
cate the character of the course in teaching history' to begin- 
ners. We present also a brief statement of the method to be 
employed in actual instruction. 

Teachef's Sfafement. — The teacher will state but a few 
facts at a time, and then have the pupils repeat these facts. 
He will then state a few more facts, and have them repeated. 
Then haA^e both groups of facts repeated; and then proceed 
to a new statement. It is a mistake to repeat too mau}^ facts 
at one time, as the pupils' minds will begin to wander, 
and very little will be vmderstood or retained. When the 
lesson is a connected narrative, the unbroken statement may 
be longer, as the interest of the stor}' will hold the pupils' at- 
tention. • 

Teacher's 3faimer, — The teacher's manner should be con- 
versational. He should be careful to avoid a mechanical and 
declamatory' method of speaking. Do not attempt to give 
lectures on history to little children. We have seen teachers 
take all the interest out of the subject by the neglect of this 
simple suggestion. There should be a plain narration of facts, 
in a simple conversational style, as if the teacher were talking 
familiarly with the pupil. He should also endeavor to portray 
the events so that they will stand out as pictures before the 
child's mind, and seem not like a school-room task, but like a 
renlity, to them. 

JfupiVs Recitation The pupil's statement should be 



TEACHING HISTORY. 498 

partly topical and partlj' interrogative. Call on one to tell 
all he can, and then on another to adil what maj- be omitted, 
and then on another, etc. Let one tell one thinu;, and another 
another thing, when the lesson can be naturally divided into 
parts. It is interesting to see how the eyes will flash as a 
new fact rises into the memory which was forgotten by the 
pnpil reciting. When there are fticts not remembered, let the 
teacher call them ont by appropriate questions. Then, after 
all the facts are brought before the mind again, let some one 
give the whole story, connecting all the events together in 
their proper order. Do not be afraid, with little children, to 
have them tell the story over and over, as their interest in 
the relation will prevent their tiring of the facts related. 

Hioffraphtj. — The teacher should remember to make ])iog- 
raphy, so far as possible, the basis of history. He should tell 
the pupils about Columbus, his birth, travels, disappoint- 
ments, voyages, triumphs, disgrace, etc. Tell them of Isabella 
and her jewels, of Captain John Smith and his adventures, of 
Pocahontas and her touching fate, of Henry Hudson, Miles 
Standish, Roger Williams, William Penn, Lord Baltimore, 
etc., and make the historic events cluster around these per- 
sonalities. Coming down later, we will see that stories of 
Adams, Warren, Patrick Henry, Washington, Jefferson, etc., 
will unfold the history of the- Revolution and the establish- 
ment of the nation. The stirring events of the Rebellion can 
be unfolded from a i-ecital of the personal actions of Lincoln, 
Grant, Lee, Jackson, Sherman, etc. 

Blackboard, etc. — Tlie teacher should use tlie blackboard 
to indicate the location and relation of the principal events. 
The routes of voyagers, the march of an army, the lino of 
battle, the location of forces, etc., can all be represented on 
tlie board. Historical charts, pictures, engravings, etc., will 
add interest to the description of places, persons, and events. 

Outline. — Tlie teacher should have an outline of the course 
in the elements of history to guide him in his work. This 



49-1 METHODS OF TEACHING. 



outline he can fill up from his memory, or by reading espe^ 
cially for the purpose. Such an outline will give definiteness 
and system to his instructions, which is a point not to be lost 
sight of. In our Model School, where the outlines of history 
are taught a year or two without the text-book, we place in 
the hands of our student-teachers an outline of the course, 
and require them to fill out and follow this outline in their 
instructions. 

Children Mead Histories. — Children should be encour- 
aged to read some suitable books on historical subjects. It 
is difficult to find works adapted to the capacity and taste of 
young children, many of the works written for this pur- 
pose being beyond their comprehension. Abbott's histories, 
though written for the young, are better adapted to adults 
than to children. Even Dickens's Ghild^s History of England 
can hardly be read with interest b}'- a child under twelve years 
of age. Such works as Miss Yonge's Little Duke and Prince 
and Page^ Peter Pai'ley's histories, or Goodrich's ChiWs 
History of the United States, may be read by children with 
absorbing interest. It will be well to allow pupils who have 
been reading any little work on history, to relate to the class 
what they remember of it. The teacher should often read 
historic nari'atives to the class, and have them repeat the 
same. 

Narratives. — The histories for children to read should be 
written in the form of narratives. Children take special de- 
light in the stories of history. They love to read about 
Columbus and his discovery of America, about Isabella and 
her jewels, about John Smith and his wonderful adventures, 
about CorteZ, and Pizarro, and Alfred the Great, and Wallace, 
and Bruce, etc. An historical story like The Little Duke will 
be read and reread by a child until it is committed to memory. 
The author who will write a series of such books for children, 
and really adapt them to the minds of children, will confer a 
great boon on the boj^s and girls of the country. 



% 



TEACniXG HISTORY. 495 

II. Teaching Advanced History. 

By the Advanced Course in History, we mean a course in 
which pupils are required to study the lessons in a text-book 
and recite them. The course should include the history of 
our own country, the histories of England and France, and a 
Avork on General Histoiy. It may be more or less full, accord- 
ing to the advancement of the pupils and the nature of the 
school. In treating this part of the subject we shall speak of 
the Nature of the Text-book and Recitation in History 

I. Nature of the History. — The first requisite in teaching 
history is a good text-book. History is one thing, and the 
manner of presenting it is another tiling. The events may be 
presented in a variety of ways, and the value of a text-book 
depends almost altogether upon tlie manner in which the facts 
are stated. We shall mention briefly the characteristics of a 
good text-book on histor3^ 

Sijsteinatic. — The text-book should contain a systematic 
presentation of the subject. In the primary course, history 
was presented in fragments ; in this course there should be a 
narration of continuous and connected events. Among the 
multitude of historical facts, this is not easy to accomplish ; 
and the skill of an author is especially shown in so selecting 
and connecting the events that the pupil may have a continued 
narrative and see the relation of all the parts. 

The Sti/le. — A work on histcny should be written in a clear 
and simple style. This is an important suggestion, as in no 
text-book is there a greater temptation to redundancy and an 
inflated form of expression. It is a requisite, however, often 
overlooked or not attained. Many of our text-books on his- 
tory are so complicated in their forms of expression that the 
young pupil can scarcely understand them ; and an attempt 
to recite a lesson from them results in repeating, parrot-like, 
the words of the text-book. Even in the historical works of 
the great masters, the style is often too ornate and involved. 



496 METHODS OF TEACHING, 

Macaala3^'s style is better adapted to oratory than history ; 
and others have attempted to rival his brilliant periods. The 
ideal historic style is that of Bancroft and Prescott; and for 
school histories no one has excelled Goodrich. 

Leaffing Events. — The text-book in history should px'esent 
the great leading events of the country of which it treats. All 
of history cannot be remembered ; and the first object is to 
fix the outlines of the principal facts in the mind of the 
learner.. To burden the memorj- of the pupil with details, will 
result in giving no well-connected knowledge of anything. 
Excessive minuteness of statement in a text-book on history 
is always a source of vexation to teacher and pupil. We need 
a skillful grouping of facts, which, though breaking the chron- 
ological connection, shows the relation of the events described. 
It is often well to distinguish between the more important and 
tlie less important facts b}^ a diffei'ence in the type of the text- 
book. Mere epitomes, however, aiming to cover the whole 
ground, are not satisfactory ; the use of an epitome is like 
giving a child an " index to learn by heart." 

Biof/i-aphy. — The basis of history is biography. Every 
great event of history is associated with the lives of some 
p;reat men who led the movement. Man makes histor}', and 
the centre of every great historic event is a man. Lamartine 
says, "History is neither more nor less than biography on a 
large scale." History, therefore, cannot be correctl}^ written 
"without referring to the men who created it. What means the 
history of the Dutch Republic without William of Orange at its 
centre, or the history of the Commonwealth without Crom- 
well ? Besides this, young people are especially interested in 
the lives of individuals. They can sympathize with the actions 
and feelings of a person better than with those of a societ\' or 
a nation. The lives of great men must, therefore, be inter- 
woven into the text of our school histories. 

Jlisforic Centres. — The subject should be presented in the 
form of epochs, or historic centres. In every country there 



TEACIIIXG HISTORY. 4i'^7 

are great prominent events which stand as the centres about 
which chaster the minor events. It is these great events that 
we need to flx in the memory with tlicir dates. They stand 
as "historical nnclei;" and when well established in the mem- 
ory, will suggest the facts related to them and growing out 
of them. Thus, the Age of Augustus, the Age of Elizabeth, 
the Reformation, the Crusades, etc., are suggestive of many 
accompanying events in general history. In the history of 
the United States, such divisions as Discoveries, Settlements, 
the French and Indian War, the Revolution, will serve as the 
b.isis of the historic record. 

Lioeli/ Pictures. — The text-book on history should present 
lively pictures of the past. A mere dry statement of histor- 
ical facts is a very dry thing for a child to study. We need 
moi'e than the dry bones of the subject, more than a skeleton ; 
we need a body of facts animated with a living soul. History 
can be made as interesting as fiction, and if so presented it 
would prevent our young people from wasting so much time 
over the trashy works of modern fiction. For reading, the 
historic novel, such as Scott's, Yonge's, and Muhlbajh's is 
highly recommended to the student. The text-book on his- 
tory can catch some of this spirit, even if it must be more 
systematic and condensed. The events of history should be 
made to move before the mind of the student like the pictures 
of a panorama. 

Maps and Charts. — The text-book on history shoukl con- 
tain cai'efully-prepared maps to indicate the location and re- 
lation of the events described. This is a very important 
suoirestion: it is a 2:reat defect of a text-book to be deficient 
in good maps. Maps would also be of great advantage to 
the larger works on histor}', written for adult readers, for it 
is verv unsatisfactory to spend time in searching for a map 
representing the country at the time of the events narrated. 
Historical charts, either in the Xtook or in the form of maps or 
atlases, are also of great value in teaching history. 



498 METHODS OF TEACUINQ. 

Illustrations. — The text-book on history should be copi- 
ously illustrated. Many things referred to cannot be de- 
scribed so that the pupil will obtain a clear idea of them. A 
good engraving will often give almost as accurate an idea as 
the object itself. Pictures of the Indians, of their wigwams, 
their bows and arrows, their writing upon the rocks, etc., 
convey a ver^^ correct notion of the things represented. Even 
representations of celebrated buildings or places, portraits of 
eminent men, illustrations of some prominent event, will aid 
the pupil in gaining a clear conception of the subject and in 
fixing the events in his memorj''. 

Wars, Kings, etc. — School histories should not be a mere 
record of- wars, and the names and lineage of sovereigns. 
The committing of these to memory, some one has truthfully 
observed, is in no proper sense the stud}^ of history. But the 
historian must Idc equally careful to avoid the opposite error 
of omitting those great military events and characters which 
have, to so large an extent, guided the current of history. 
Kings, queens, courts, great leaders, battles, and sieges, have 
so largely decided the fate of nations and the progress of 
civilization, that they cannot be lightly touched upon hy one 
seeking to know the great events of history and understand 
their causes. " In all times past, the lives of a few great men 
have formed the warp of history, while those of the masses 
have been but the filling." 

Cause and Effect. — The events of history are the results 
of facts and influences which have acted as their causes. The 
mind, in contemplating these facts, naturally looks backward 
and inquires after the events which caused them. The student 
of history also endeavors to penetrate the future, and predict 
the coming events as the results of present conditions. In 
other words, he delights in dealing with the causes and effects 
of historical events. The facts of history thus prepare and 
lead naturally towards the philosophy of history. 

The text-book should recognize this want, and endeavor to 



TEACHIN-Q HISTORY. 499 

meet it. While there can be no formal treatment of the 
philosophy of historj'^, the general relation of events with re- 
spect to causes and effects should be indicated. The pupil 
should be led to see the baneful results of ambition, the dis- 
honor of a nation through the violation of justice, the events 
which brought about a revolution, the causes which resulted 
in a decline or advance of freedom, etc. History will thus be 
what it has been so happily styled, " Philosophy teaching by 
example." It thus becomes a great moral teacher, lays the 
foundation of intelligent citizenship, and cultivates an appre- 
ciation of liberty and the means of preserving it. 

General Hlstorij. — In works on General History, two 
methods may be used, the ethnographic and the synchronistic. 
The Ethnographic Method describes each nation in succession 
throughout its entire histor}'. The Synchronistic Method 
groups the historic events into periods or epochs, and nar- 
rates the events of such a period, each nation coming in 
where it belongs in the period. In ancient history, the eth- 
nographic method must be mainly used, as the nations were 
essentially separate, appearing upon the stage at successive 
periods, and rarely joining in an}^ one general movement. In 
some cases, however, as in the history of the states of Greece, 
the synchronistic method must be mainly followed. 

In many cases, the historic movement is carried along by 
some particular nation, as the representative, for the time 
being, of some controlling idea or principle, the other nations 
playing a subordinate part. In other cases, the nations share 
very nearly equally in the progress of events, no one occupy- 
in'g the prominence of leadership in the movement. In both 
of these cases, the S3'^nchronistic method is preferable. It is 
often necessary, however, to make a compromise between the 
ethnographic and s^-nchronistic methods. 

In histories written for young pupils, .the ethnographic 
method is usually preferable. The description of periods will 
often give only a confused picture of the whole. A pupil 



500 METHODS OF TEACHING. 

needs to have a good general outline fixed in his mind before 
he can well attend to the grouping. He must first attend to 
the order of time, or his subsequent reading and study will 
be embarrassed. The grouping of the details of the history 
of each individual nation around some central epoch is similar 
to a generalization from facts in the natural sciences, and 
naturally follows a knowledge of the facts themselves. 

II. The Recitation in History. — The Recitation in His- 
tory should be modified by and adapted to the study. It 
I'esembles in many respects the recitation in geography, 
though it is less technical and requires more continued narra- 
tive than most subjects in geography. It adds the element 
of time to place, and thus moves with a current of events. 
The subject of history allows perhaps as little A^ai'iet}' in the 
recitation as any subject taught ; and j'et it requires talent 
and skill of a high order for real artistic teaching. 

Teacher's Preparation. — The teacher must be thoj'oughly 
prepared on the subject of history. He should be familiar 
with all the leading events and their relation to one another ; 
and be well prepared also on the details of the special subject 
he is teaching. He must also be thoroughly' acquainted with 
the text-book he is using ; he must know what facts the 
author presents, the order in which they are given, and the 
amount of details into which he enters. This is a necessity 
in good teaching; no one can hear, satisfactorily, a lesson 
prepared in a given text-book, unless he knows the text-book 
himself. The teacher must thus be master of the text-book 
as well as of the subject. 

The teacher should also be a good talker. He should not 
only know the facts, but should learn how to present them in 
a lively and interesting manner. In no class is a ready and 
brilliant talker so necessary as in history. The teacher should 
have a fund of biographical incident, of interesting personal 
anecdotes, and a happy talent for description. 

Pupil's Preparation. — In preparing a lesson in history, 



TEACHING HISTORY. 501 

the pupils should first read over the lesson and obtain a gen- 
eral idea of the leading events. They should then fill up tiie 
details, linking them in their proper order. The words of tiie 
text-book should not, as a rule, be committed; though happy 
and choice forms of expression may be memorized. A mere 
committing of the language, as is too often the case with 
])upils in our histor}^ classes, is altogether wrong. An effort 
should be made to see the relation of the events so that they 
are not remembered as isolated facts, but that one fact shall 
suggest another. In many cases, the writing of an outline 
will aid in preparing for the recitation. 

Tiypical Recitation. — The recitation in history should be 
mainly topical. A pupil should be called upon to recite the 
first topic, another the next topic, another to take up the nar- 
rative where the previous pupil leaves it off, and so on 
throughout the lesson. The oixler of events in the text is to 
be closely followed, though there should be no slavish depend- 
ence on the book. The pupils should be encouraged to ex- 
press the facts in their own language, bearing in mind that it 
is a clear conception of events that is required. At the close 
of a topic, omissions may be supplied and corrections made 
by the class and the teacher. 

Order of Recitation. — The recitation should usually pro- 
ceed in the order of the occurrence of the events. It may also 
begin at a certain point and trace the events backward from 
consequent to antecedent. The former method is called the 
Progressive order ; the latter, the Regressive order. The pro- 
gressive method is preferable for the first statement of the 
lesson ; the regressive method may be used for the re-state- 
ment of a lesson. The regressive method is especially suit- 
able for a general review of the events of a given period. 

Questioning. — At the close of the recitation of a toi)ic, the 
pupil should be examined on it to see that he really has a 
clear undei'standing of it, and is not merely repeating the 
text-book. The teacher should see that he has in his mind a 



502 



METHODS OF TEACHING. 



A'ivid picture of the events, and not merel}' a list of words in 
his memory. He should be required to state the leading 
events, to show their relation to one another, to trace conse- 
quences to their antecedents and antecedents to their con- 
sequences, etc. In no study is judicious questioning so 
valuable as in the recitation of history. 

Meviews. — At each recitation there should be a review of 
the important events of the last several lessons. Such a re- 
A^iew will serve to impress permanently all the great leading 
facts upon the memory, which are all that the student can be 
expected to retain. This review may be b}^ questions requir- 
ing brief answers, or the teacher may require the pupils to 
state in order the most prominent facts, etc. It may follow 
either the progressive or regressive order. 

Kew Blatter. — The teacher should add some new matter at 
nearly every recitation. This may consist of greater details 
on the topic discussed, or a statement of the relation of these 
events to contemporaneous history, or the causes of these 
events, or the results to which tliey led. The teacher should 
be all alive to the subject, and inspire his pupils with an equal 
interest. Historical knowledge, flowing from the lij^s of the 
living teacher, will make an ineffaceable impression, and, what 
is still better, cultivate a historical taste and give an ideal of 
high historical culture, which will be worth more to the pupil 
than the history he learns. 

Reading History. — Pupils should be encouraged to read 
more detailed works on the sulyect the}^ are studj-ing. Of 
course, this can be done to onl3' a limited extent, as their time 
is required for their other studies; but even a short course of 
reading will do much to cultivate a taste for histor^^ and 
awaken a desire, to continue the study, and to make them- 
selves familiar with the leading events in the history of the 
world. If the school course in history accomplislied no other 
obj-ect than to awaken an interest in historical reading, it 
would accomplish a great work. 



TEACHIXQ HISTORY. 503 

Discussions. — Pupils should be encouraged to reflect upon 
the actions of men and nations, and express the opinions thus 
formed. Was the action under the circumstances right? 
What would have been the probable result had another course 
been taken? What do you admire in the character of Colum- 
bus? Of Washington? Of Jefferson? Of Adams? A discus- 
sion on some historical event upon which opposite sides are 
taken is also recommended. Such exercises will give a 
reality to the study, awaken a deeper interest in it, and tend 
to fix it more permanently in the memory. 

The Dates. — The question is often asked, Should the dates 
be committed to memory ? Dates are neccssarj- ; we not only 
wish to know the event, but when it took place. Still, all 
dates cannot be remembered, and to memorize the dates of 
isolated events is worse than useless. (The dates of certain 
leading events should be fixed in the memory.^ These become 
as centres or nuclei to which other events may be referred, 
and their approximate time remembered. Some dates should 
be remembered exactly, others may be committed in " round 
numbers." The proper relation of incidents will aid in re- 
membering the time at which the}^ occurred. 

Cause and Effect. — The teacher should cultivate in tlie 
pupil the habit of tracing causes and effects in history. The 
time has gone b}' when a history lesson should be made a 
mere recital of events. We need not only to know history 
but to learn the lessons of history. "All history," says Croly, 
"is but a romance unless it is studied as an example." Dr. 
Currie also truthfully remarks, " The ultimate design of study- 
ing history is not only to acquire knowledge, but to form the 
judgment so that it shall be able to apply the lessons of past 
time to the present;" and the teacher of history should bear 
this in mind and govern himself accordingl3^ A fact is dead 
until it is taken up into the organic lite of human society, 
and becomes a part of that grand organism which stands 
before the mind in a true conception of history. 



504 METHODS OF TEACHING. 

Maps ami CJtfivfs. — A ^•ood set of historical mnps and 
charts wouhl be invalMable in teaching history. The inaps 
should be large enough to hang up before the class and be used 
in the recitation. The pupil should be required to locate the 
events, trace them from one point to another, show the inarch 
of armies, the location of battle-fields, the wanderings of ex- 
plorers, the course of emigration, etc. Charts are of especial 
advantage in general history, by showing the chronological 
relations, each nation and event being indicated in time as 
countries are represented in space on a map. Frogressive 
maps, showing the states and countries, their extent and 
boundaries at different periods, are also of great value. 

Lectures. — Lectures on history in connection with their 
regular lessons, or at the close of a school course, are benefi- 
cial. With young pupils, they should be made conversational, 
and the leading events be outlined upon the board for them to 
copy. With more advanced pupils, the lectures may be more 
formal and continuous. No complete record of notes should 
be required, as the attempt to take notes will break the threijd 
of tlieir thought and thus mar the effect of the lecture. But 
little accurate knowledge of history can be left on the mind 
by a lecture ; the principal value is to ar'ouse an interest and 
leave in the mind those general impressions which prepare for 
a more detailed study of the subject. The most interesting 
topics for historical lectures are tlie lives and times of some 
eminent person, and the development of those theories called 
the Philosophy of History. 

Note.— The Arts of Writing, Drawing, and Vocal Music are omitted from 
this work on account of the many treatises ou them in manuals prepared for 
teachers. 



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